From 5573dc9399ca7b5ee2ff6ab127bb3e611ea066e5 Mon Sep 17 00:00:00 2001 From: Yimin Zhong Date: Wed, 21 Aug 2024 06:38:05 +0000 Subject: [PATCH] Update Awards --- .../Awards-Algebra-and-Number-Theory-2024.csv | 16 +++++++++++----- Analysis/Awards-Analysis-2024.csv | 5 +++-- .../Awards-Applied-Mathematics-2024.csv | 17 +++++++++-------- Combinatorics/Awards-Combinatorics-2024.csv | 9 ++++++--- .../Awards-Computational-Mathematics-2024.csv | 2 ++ .../Awards-Geometric-Analysis-2024.csv | 11 ++++++----- .../Awards-Mathematical-Biology-2024.csv | 18 +++++++++++++----- Statistics/Awards-Statistics-2024.csv | 3 ++- 8 files changed, 52 insertions(+), 29 deletions(-) diff --git a/Algebra-and-Number-Theory/Awards-Algebra-and-Number-Theory-2024.csv b/Algebra-and-Number-Theory/Awards-Algebra-and-Number-Theory-2024.csv index 85f8a8e..03e8254 100644 --- a/Algebra-and-Number-Theory/Awards-Algebra-and-Number-Theory-2024.csv +++ b/Algebra-and-Number-Theory/Awards-Algebra-and-Number-Theory-2024.csv @@ -1,4 +1,10 @@ "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract" +"2401256","Syzygies and Koszul Algebras","DMS","OFFICE OF MULTIDISCIPLINARY AC, ALGEBRA,NUMBER THEORY,AND COM","09/01/2024","08/20/2024","Jason McCullough","IA","Iowa State University","Standard Grant","Tim Hodges","08/31/2027","$277,690.00","","jmccullo@iastate.edu","1350 BEARDSHEAR HALL","AMES","IA","500112103","5152945225","MPS","125300, 126400","9150","$0.00","This award supports research in commutative algebra ? the study of the set of solutions of systems of multi-variate polynomial equations. Specifically, the project involves the study of free resolutions and Koszul algebras. Free resolutions are technical objects that allow us to approximate complicated algebraic objects by simpler ones. They can often be computed using computer algebra systems such as Macaulay2. Koszul algebras have particularly nice free resolutions and arise in a surprising number of contexts, especially in geometry and combinatorics. As part of this project, the PI seeks to classify certain Koszul algebras in several specific areas of interest. More broadly, the PI will supervise the training of graduate students and postdoctoral fellows. The PI will also begin work on a new textbook on commutative algebra with Macaulay2.

A free resolution of a module over a commutative ring is an acyclic sequence of free modules whose zero-th homology equals the module. In the graded setting, resolutions are unique up to isomorphism and encode useful information about the module being resolved. Koszul algebras are graded algebras over a field such that the field has a linear free resolution over the algebra. The PI seeks to establish new classes Koszul algebras related to hyperplane arrangements (via Orlik-Solomon algebras), lattices and matroids (specifically Chow rings and graded Moebius algebras), toric rings (specifically matroid base rings, in connection to White?s Conjecture), and binomial edge ideals. Additionally, the PI will study the Eisenbud-Goto Conjecture in the normal setting, where it is still an open question.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2401308","Collaborative Research: Periods and Functorial Transfer","DMS","ALGEBRA,NUMBER THEORY,AND COM","09/01/2024","08/20/2024","Omer Offen","MA","Brandeis University","Standard Grant","Andrew Pollington","08/31/2027","$200,000.00","","offen@brandeis.edu","415 SOUTH ST","WALTHAM","MA","024532728","7817362121","MPS","126400","","$0.00","Symmetries play an important role in mathematics and in physics. This research project concerns functions that are invariant under a collection of symmetries, called automorphic forms, that are connected to number theory, representation theory, harmonic analysis and string theory. The Langlands and relative Langlands programs predict subtle relations between different spaces of automorphic forms, a structure that is closely related to many questions in number theory and analysis. In this project the PIs will work together to study the Langlands and relative Langlands programs and to extend them to new situations. The PIs will also systematically collaborate on the training of PhD students and in developing graduate-student-centered seminars for them.

This project concerns functoriality and the study of periods in the Langlands and relative Langlands programs and for covering groups. The PIs, working jointly, will establish a new Shimura correspondence which is detected by a period involving a theta function. To do so, they will develop a suitable relative trace formula. Also, working jointly with Ginzburg, the PIs will study periods for the discrete, non-cuspidal spectrum, and study endoscopic lifts and periods. These projects will give new information about periods of automorphic forms and will add to the understanding of relative trace formulas. They naturally complement recent advances for reductive groups and the relative Langlands program and by including covering groups they will broaden our understanding of these topics. The PIs will also contribute to graduate training and to the nation?s development of a diverse, globally competitive STEM workforce.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2401172","RUI: Arithmetic Dynamics: Algebraic and Analytic","DMS","ALGEBRA,NUMBER THEORY,AND COM","09/01/2024","08/19/2024","Robert Benedetto","MA","Amherst College","Standard Grant","Adriana Salerno","08/31/2027","$200,000.00","","rlbenedetto@amherst.edu","155 S PLEASANT ST","AMHERST","MA","010022234","4135422804","MPS","126400","9251","$0.00","Arithmetic dynamics is a mathematical field bridging the interface between number theory and dynamical systems. It concerns a broad range of algebraic questions about rational functions and polynomial equations that arise, along with the more analytic aspects of chaos and fractals, in the iteration of nonlinear functions. This project will focus on subtle open problems in this rich area, including the consideration of both the algebraic and the analytic aspects, along with the interactions between them. In addition, the PI will supervise two undergraduate students in a summer research REU experience, to expand their mathematical training. Any computational data and theoretical results from any part of this project will be shared via websites such as ArXiv.org, published in peer-reviewed mathematical journals, or otherwise disseminated openly to the broader mathematical research community.

The dynamical systems studied here are defined by repeatedly composing a polynomial or rational function with itself. A wide range of chaotic properties arise under such iterations. The algebraic questions the PI will study in this project mainly concern the action of number-theoretic objects known as Galois groups on backwards orbits, which are natural dynamical objects. The analytic questions the PI will study concern the variation of a range of dynamical objects (especially the intricate fractals known as Julia sets) in a family of such dynamical systems, when working over a so-called non-archimedean field. These two sides of the project are tied together by p-adic dynamics, one of the PI's main areas of expertise; p-adic number fields comprise a fundamental example of non-archimedean fields. On the algebraic side, p-adic dynamical features for different prime numbers p can elucidate Galois actions. On the analytic side, the appropriate setting for p-adic and more general non-archimedean dynamics is the Berkovich projective line, another of the PI's areas of expertise. In both cases, the PI's application of p-adic dynamical tools promises to provide new insights into the unpredictable behavior of complicated arithmetic dynamical systems.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2401309","Collaborative Research: Periods and Functorial Transfer","DMS","ALGEBRA,NUMBER THEORY,AND COM","09/01/2024","08/20/2024","Solomon Friedberg","MA","Boston College","Continuing Grant","Andrew Pollington","08/31/2027","$66,667.00","","friedber@bc.edu","140 COMMONWEALTH AVE","CHESTNUT HILL","MA","024673800","6175528000","MPS","126400","","$0.00","Symmetries play an important role in mathematics and in physics. This research project concerns functions that are invariant under a collection of symmetries, called automorphic forms, that are connected to number theory, representation theory, harmonic analysis and string theory. The Langlands and relative Langlands programs predict subtle relations between different spaces of automorphic forms, a structure that is closely related to many questions in number theory and analysis. In this project the PIs will work together to study the Langlands and relative Langlands programs and to extend them to new situations. The PIs will also systematically collaborate on the training of PhD students and in developing graduate-student-centered seminars for them.

This project concerns functoriality and the study of periods in the Langlands and relative Langlands programs and for covering groups. The PIs, working jointly, will establish a new Shimura correspondence which is detected by a period involving a theta function. To do so, they will develop a suitable relative trace formula. Also, working jointly with Ginzburg, the PIs will study periods for the discrete, non-cuspidal spectrum, and study endoscopic lifts and periods. These projects will give new information about periods of automorphic forms and will add to the understanding of relative trace formulas. They naturally complement recent advances for reductive groups and the relative Langlands program and by including covering groups they will broaden our understanding of these topics. The PIs will also contribute to graduate training and to the nation?s development of a diverse, globally competitive STEM workforce.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2401536","Global cohomological approaches to L-functions","DMS","ALGEBRA,NUMBER THEORY,AND COM","09/01/2024","08/19/2024","Kiran Kedlaya","CA","University of California-San Diego","Continuing Grant","Andrew Pollington","08/31/2027","$66,828.00","","kedlaya@ucsd.edu","9500 GILMAN DR","LA JOLLA","CA","920930021","8585344896","MPS","126400","","$0.00","This award concerns Number theory, the analysis of equations involving integers and their solutions, which is one of the oldest branches of mathematics. As such, it has a long history of being driven by empirical observations; such important results as the law of quadratic reciprocity and the prime number theorem originated from numerical experiments. With an eye on the ongoing revolution in artificial intelligence, the PI will combine the latest theoretical developments in number theory with a big data approach to uncover hidden structures in the theory of L-functions. The PI will also promulgate this work through mentoring of PhD students, dissemination of advanced course materials, organization of workshops, and nonprofit governance, all with a view towards broadening participation.

The PI will study Hasse-Weil L-functions associated to algebraic varieties over number fields through a mix of theoretical and computational techniques. On the theoretical side, the PI is investigating recent evidence pointing towards a global cohomological interpretation of these L-functions, using as a test case the families of motives parametrized by hypergeometric differential equations. On the computational side, the PI is developing streamlined algorithms to compute hypergeometric L-functions, partially informed by q-de Rham cohomology; this yields a rich data set for investigating Frobenius distributions, special values, murmurations, and other phenomena.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2401470","Special Functions of p-adic Algebraic Groups and Quantum Groups","DMS","ALGEBRA,NUMBER THEORY,AND COM","09/01/2024","08/19/2024","Benjamin Brubaker","MN","University of Minnesota-Twin Cities","Continuing Grant","James Matthew Douglass","08/31/2027","$193,010.00","","brubaker@math.umn.edu","200 OAK ST SE","MINNEAPOLIS","MN","554552009","6126245599","MPS","126400","","$0.00","This is a project to develop connections between number theory and physics. A modern paradigm in number theory uses highly symmetric functions to answer the most fundamental questions about solutions of equations in several variables. Quite surprisingly, these same symmetries arise in physics, particularly statistical mechanics, where one seeks to determine global behavior of molecules based on local interactions between particles. The PI, collaborators, and students, will explain and explore further mathematical consequences of this connection. The project will provide research training opportunities for both undergraduate and graduate students.

More precisely, the bridge between number theory and statistical mechanics alluded to above is the theory of quantum groups and most of the specific projects pursued will use the representation theory of quantum group modules. To make connections with special functions in number theory, particularly matrix coefficients of algebraic groups over local fields, one needs new results on quantum group modules. The PI and collaborators will use quantum affine Lie superalgebra modules to produce lattice models with the required symmetry used in the study of matrix coefficients for metaplectic groups. In reverse, by expressing new classes of special functions from representation theory as partition functions of solvable lattice models, one obtains conjectural invariants of multi-parameter quantum groups. The primary scientific goals include deeper insight from quantum groups into various aspects of the Langlands program.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401522","Multigraded commutative algebra and asymptotic behavior of filtrations of ideals","DMS","ALGEBRA,NUMBER THEORY,AND COM","08/15/2024","08/15/2024","Jonathan Montano","AZ","Arizona State University","Standard Grant","Tim Hodges","07/31/2027","$225,000.00","","montano@asu.edu","660 S MILL AVENUE STE 204","TEMPE","AZ","852813670","4809655479","MPS","126400","","$0.00","This project focuses on several problems in commutative algebra, the branch of mathematics that explores properties of polynomial equations, which are fundamental for modeling diverse phenomena in science and engineering. As a result, commutative algebra has strong connections with biology, computer science, physics, and other quantitative fields. When equations involve multiple variables, their comprehensive study can become intractable. A powerful strategy in such cases involves decomposing polynomials into smaller pieces and using information from these components to derive general properties, a theme known as multigraded commutative algebra. Another significant approach concerns understanding the asymptotic behavior of sequences of sets of equations known as filtrations. This project will advance these research directions by addressing key questions within the field. Furthermore, this project will have a broader impact on the postdoctoral, graduate, and undergraduate student population through mentoring initiatives and the organization of seminars, conferences, and workshops.


The project will advance the understanding of Hilbert series through a detailed investigation of multidegree support and K-polynomials of multiprojective schemes. This research will explore connections between the topology of schemes and the combinatorial aspects of K-polynomials, with direct implications for Schubert geometry, toric geometry, and multiparameter persistent homology. Additionally, the project will employ Presburger and Ehrhart methods to analyze the quasi-polynomial behavior of homological functors applied to multigraded modules. Divisorial filtrations, which are defined via valuations, exhibit intricate geometric properties and include significant examples such as symbolic powers and integral closure powers of ideals. The project will study the growth rate of the number of generators of these filtrations. Furthermore, the project will investigate whether divisorial filtrations are F-split, potentially indicating mild F-singularities in their blowup algebras and low complexities in the growth of homological functors.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2346615","Conference: Zassenhaus Groups and Friends Conference 2024","DMS","ALGEBRA,NUMBER THEORY,AND COM","01/01/2024","11/08/2023","Yong Yang","TX","Texas State University - San Marcos","Standard Grant","Tim Hodges","12/31/2024","$18,000.00","Thomas Keller","yy10@txstate.edu","601 UNIVERSITY DR","SAN MARCOS","TX","786664684","5122452314","MPS","126400","7556","$0.00","This award supports participation in the 2024 Zassenhaus Groups and Friends Conference which will be held at Texas State University in San Marcos, TX. It will take place on the campus of the university from noon of Friday, May 31, 2024, to the early afternoon on Sunday, June 2, 2024. It is expected that about 40 researchers will attend the conference, many of whom will give a talk.

The Zassenhaus Groups and Friends Conference, formerly known as Zassenhaus Group Theory Conference, is a series of yearly conferences that has served the mathematical community since its inception in the 1960s. The speakers are expected to come from all over the country and will cover a broad spectrum of topics related to the study of groups, such as representations of solvable groups, representations of simple groups, character theory, classes of groups, groups and combinatorics, recognizing simple groups from group invariants, p-groups, and fusion systems.

The conference will provide group theory researchers in the US a forum to disseminate their own research as well as to learn about new and significant results in the area. The conference will provide a particularly inviting environment to young mathematicians and will inspire future cooperation and collaborations among the participants. It is expected that it will have great impacts on the group theory research community. The organizers will make great effort to attract a demographically diverse group of participants including women and racial and ethnic minorities. More information can be found at the conference website, https://zassenhausgroupsandfriends.wp.txstate.edu/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401382","Building Blocks for W-algebras","DMS","ALGEBRA,NUMBER THEORY,AND COM","09/01/2024","08/07/2024","Andrew Linshaw","CO","University of Denver","Standard Grant","James Matthew Douglass","08/31/2027","$204,985.00","","andrew.linshaw@du.edu","2199 S UNIVERSITY BLVD RM 222","DENVER","CO","802104711","3038712000","MPS","126400","","$0.00","Vertex operator algebras (VOAs) arose in physics in the 1980s as the symmetry algebras of two-dimensional conformal field theories (CFTs) and were first defined mathematically by Borcherds. They have turned out to be fundamental objects with connections to many subjects including finite groups, Lie theory, combinatorics, integer partitions, modular forms, and algebraic geometry. W-algebras are an important class of VOAs that are associated to a Lie (super)algebra g and a nilpotent element f in the even part of g. They appear in various settings including integrable systems, CFT to higher spin gravity duality, the Allday-Gaiotto-Tachikawa correspondence, and the quantum geometric Langlands program. In this project, the PI will investigate the structure and representation theory of W-algebras. This will advance the subject and provide research training and collaborative opportunities for graduate students and postdocs.

In more detail, principal W-algebras (the case where f is a principal nilpotent) are the best understood class of W-algebras. They satisfy Feigin-Frenkel duality, and in classical Lie types they also admit a coset realization which has numerous applications to representation theory. It turns out that both Feigin-Frenkel duality and the coset realization are special cases of a more general duality which was conjectured by Gaiotto and Rapcak and proven recently by the PI and Creutzig. It says that the affine cosets of certain triples of W-algebras are isomorphic as 1-parameter VOAs. These cosets are known as Y-algebras in type A, and orthosymplectic Y-algebras in types B, C, and D. The Y-algebras can all be obtained as 1-parameter quotients of a universal 2-parameter VOA, and they are conjectured to be the building blocks for all W-algebras in type A. The orthosymplectic Y-algebras are quotients of another universal 2-parameter VOA, but they are not all the necessary building blocks for W-algebras in types B, C, and D. The main goals of this project are (1) to identify the missing building blocks, which we expect to arise as quotients of a third universal 2-parameter VOA; (2) to prove that W-algebras of all classical types can be obtained as conformal extensions of tensor products of building blocks. Special cases will involve W-algebras with N=1 and N=2 supersymmetry, and the PI hopes to prove some old conjectures from physics on coset realizations of these structures. Finally, the Y-algebras and other building blocks admit many levels where their simple quotients are lisse and rational. Exhibiting W-algebras at special levels as extensions of building blocks will lead to many new rationality results.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -26,10 +32,10 @@ "2401662","Conference: Southern Regional Algebra Conference 2024","DMS","ALGEBRA,NUMBER THEORY,AND COM","03/15/2024","01/18/2024","Jean Nganou","TX","University of Houston - Downtown","Standard Grant","Tim Hodges","02/28/2025","$14,990.00","","nganouj@uhd.edu","1 MAIN ST","HOUSTON","TX","770021014","7132218005","MPS","126400","7556","$0.00","This award supports participation in the Southern Regional Algebra Conference (SRAC). The SRAC is a yearly weekend conference that has been in existence since 1988. Its first edition was held at the University of Southern Mississippi in the Spring of 1988. This spring the SRAC will be held at the University of Houston-Downtown, March 22-24, 2024. The SRAC brings together mathematicians that carry out research in the area of algebra and closely related areas for a full weekend of lectures, short presentations and discussions. The conference attracts researchers from many undergraduate institutions in the Gulf Coast Region that usually do not have sufficient funding to support their research activities, especially long-distance meetings. It is also an important platform for graduate students and early career mathematicians to present their research in algebra and be exposed to a community of algebraists outside their respective home institutions.

The main themes of the conference are Lie/Leibniz Algebras and their representation theory; and the theory of nearrings and other generalizations of rings. On Friday March 22, there will be a single session on topics in algebra that lie either at the intersection of two themes of the conference or outside of their union. On Saturday March 23, the conference will begin with an hour-long plenary session on Leibniz algebras and the rest of the day will be split into two parallel sessions of 25-min talks, with each session focusing on one of the main themes. On Sunday March 24, the conference will start with an hour-long plenary session on the near-rings theory, and the rest of the morning will be split into two parallel sessions of 25-min talks, with each session focusing on one of the main themes. There will be plenty of opportunity for informal follow-up discussions. Further information is available at the conference website:
https://www.uhd.edu/academics/sciences/mathematics-statistics/southern-regional-algebra-conference.aspx

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2426080","Conference: Motivic homotopy, K-theory, and Modular Representations","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","07/15/2024","07/08/2024","Aravind Asok","CA","University of Southern California","Standard Grant","Swatee Naik","06/30/2025","$31,500.00","Paul Sobaje, Julia Pevtsova, Christopher Bendel","asok@usc.edu","3720 S FLOWER ST FL 3","LOS ANGELES","CA","90033","2137407762","MPS","126400, 126700","7556","$0.00","This award provides partial support for the participation of early career US-based mathematicians to attend the conference ""Motivic homotopy, K-theory, and Modular Representations"" to be held August 9-11, at the University of Southern California in Los Angeles, California. While recent events have often focused on specific aspects within these domains, this conference aims to unite mathematicians from diverse yet interconnected areas. The core purpose of the project is to support the attendance and career development of emerging scholars from the United States, and support from this award will benefit scholars from a broad selection of U.S. universities and diverse backgrounds; the intent is to maximize the effect on workforce development.

The conference will convene at the intersection of homotopy theory, algebraic geometry, and representation theory, focusing on areas that have experienced significant growth over the past three decades. Furthermore, it will explore applications of these fields to neighboring disciplines such as mathematical physics. All these fields have seen major advances and changes in the last five years, and this conference with international scope aims to synthesize major recent developments. More information about the conferences can be found at the website: https://sites.google.com/view/efriedlander80.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401444","Conference: Workshop on Automorphic Forms and Related Topics","DMS","ALGEBRA,NUMBER THEORY,AND COM","03/01/2024","02/27/2024","Melissa Emory","OK","Oklahoma State University","Standard Grant","Andrew Pollington","02/28/2025","$24,800.00","Kimberly Logan, Liyang Yang, Jonathan Cohen","melissa.emory@okstate.edu","401 WHITEHURST HALL","STILLWATER","OK","740781031","4057449995","MPS","126400","7556, 9150","$0.00","The 36th Annual Workshop on Automorphic Forms and Related Topics (AFW) will take place May 20-24, 2024, at Oklahoma State University in Stillwater, OK. The AFW is an internationally recognized, well-respected conference on topics related to automorphic forms, which have played a key role in many recent breakthroughs in mathematics. The AFW will bring together a geographically diverse group of participants at a wide range of career stages, from graduate students to senior professors. Typically, about half of the attendees at the AFW are at early stages of their careers, and about one quarter to one third of participants are women. The AFW will continue to provide a supportive and encouraging environment for giving talks, exchanging ideas, and beginning new collaborations. This is the first time the AFW will meet in Oklahoma where many experts on automorphic forms and closely related topics are nearby. Thus, in addition to attracting speakers who participate annually, the workshop is likely to draw a mix of new attendees who will contribute new perspectives and energy and benefit from the workshop. The workshop is known for its inclusive, encouraging atmosphere, particularly to early career researchers and to those from underrepresented groups in the number theory community. The workshop has traditionally been a fruitful place for these researchers to connect with potential collaborators and mentors at other institutions, working on related topics. To help achieve this goal, the 2024 AFW will feature five expository talks on various fundamental topics in the theory of automorphic forms, aimed at the graduate student level. There will also be two panel discussions focused on mathematical career questions.

Automorphic forms play a central role in number theory, being integral to the proofs of many groundbreaking theorems, including Fermat's Last Theorem (by Andrew Wiles), the Sato-Tate Conjecture (by Thomas Barnet-Lamb, David Geraghty, Michael Harris, and Richard Taylor), Serre's Conjecture (by Chandrashekhar Khare, Mark Kisin, and Jean-Pierre Wintenberger), the Sato-Tate Conjecture (by Thomas Barnet-Lamb, David Geraghty, Michael Harris, and Richard Taylor), Serre's Uniformity Conjecture (by Yuri Bilu and Pierre Parent), and the Fundamental Lemma (for which Ngo Bau Chau was awarded the Fields Medal). Automorphic forms are the subject of many important ongoing conjectures, among them the Langlands program, connections to random matrix theory, and the generalized Riemann hypothesis. They also appear in many areas of mathematics outside number theory, most notably in mathematical physics. The topics covered in this year's workshop are likely to include elliptic, Siegel, Hilbert, and Bianchi modular forms, elliptic curves and abelian varieties, special values of L-functions, p-adic aspects of L-functions and automorphic forms, connections with representation theory, mock modular forms, quadratic forms, connections with mathematical physics, monstrous moonshine, and additional related areas of research.


Additional information can be found on the conference website: http://automorphicformsworkshop.org/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2414452","Collaborative Research: Conference: Special Trimester on Post-Quantum Algebraic Cryptography","DMS","ALGEBRA,NUMBER THEORY,AND COM, Secure &Trustworthy Cyberspace","09/01/2024","07/02/2024","Delaram Kahrobaei","NY","CUNY Queens College","Standard Grant","Tim Hodges","08/31/2025","$10,000.00","","dkahrobaei@gc.cuny.edu","6530 KISSENA BLVD","FLUSHING","NY","113671575","7189975400","MPS","126400, 806000","025Z, 7556","$0.00","This award funds participation by US-based researchers in a special trimester on Post-quantum algebraic cryptography, to be held at the The Henri Poincare Institute, Paris, France, September 9 - December 13, 2024. In recent years, there has been a substantial amount of research on quantum computers -- machines that exploit quantum mechanical phenomena to solve mathematical problems that are difficult or intractable for conventional computers. If large-scale quantum computers are ever built, they will be able to break many of the public-key cryptosystems currently in use. This would seriously compromise the confidentiality and integrity of digital communications on the Internet and elsewhere. The goal of post-quantum cryptography is to develop cryptographic systems that are secure against both quantum and classical computers, and can interoperate with existing communications protocols and networks. The thematic trimester program will bring together researchers and practitioners from academia, industry, and government institutions with diverse backgrounds to discuss quantum algorithms, quantum-safe cryptography, as well as deployment issues, from different angles.

This thematic trimester program will address various proposed cryptographic primitives that are currently considered to be quantum-safe. This includes lattice-based, multivariate, code-based, hash-based, group-based, and other primitives some of which were considered by NIST during their post-quantum standardization process. Our program will also address various functionalities of cryptographic constructions that are in high demand in real life. This includes fully homomorphic encryption that provides for private search on encrypted database and machine learning on encrypted data. Another functionality that is getting increasingly popular is outsourcing (a.k.a. delegating) computation of algebraic functions including group exponentiation, product of group exponentiations, etc., from a computationally limited client holding an input and a description of a function, to a computationally stronger entity holding a description of the same function. Further information can be found at the program website:
https://www.ihp.fr/en/events/post-quantum-algebraic-cryptography-paris

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2412921","Conference: CAAGTUS (Commutative Algebra and Algebraic Geometry in TUcSon)","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","02/14/2024","Debaditya Raychaudhury","AZ","University of Arizona","Standard Grant","Tim Hodges","04/30/2025","$15,000.00","Arvind Suresh, Zhengning Hu","draychaudhury@math.arizona.edu","845 N PARK AVE RM 538","TUCSON","AZ","85721","5206266000","MPS","126400","7556","$0.00","This award will support participation in a weekend conference to be held at the University of Arizona, Tucson on May 4 - 5. The aim of the conference is to establish a solid basis for contacts and collaborations among researchers in Commutative Algebra and Algebraic Geometry located in Arizona and its neighboring states. Its main purposes are to stimulate new directions of research, to provide opportunities to junior researchers to share their work, and to provide a venue for networking and collaboration in the southwest. Its other aim is to expand the network of algebraic and arithmetic geometers by providing an algebro-geometric complement of the Arizona Winter School.

The conference plans to host four leading researchers from Arizona and its neighboring states working in Commutative Algebra and Algebraic Geometry, who will give colloquium-style one-hour lectures on their respective areas of expertise. These hour-long lectures are expected to provide surveys of the current state of the research in these areas, and to provide suggestions for new avenues of research. There will be five or six 30-minute talks given by young researchers, as well as six to eight contributed short 20-minute talks and a poster session. Priority for these contributed talks and posters will be given to recent PhD recipients and members of groups underrepresented in mathematics. Further information is available at the conference website: https://sites.google.com/math.arizona.edu/caagtus/home

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2337451","CAREER: Higgs bundles and Anosov representations","DMS","ALGEBRA,NUMBER THEORY,AND COM, GEOMETRIC ANALYSIS","07/01/2024","02/02/2024","Brian Collier","CA","University of California-Riverside","Continuing Grant","Swatee Naik","06/30/2029","$79,647.00","","brian.collier@ucr.edu","200 UNIVERSTY OFC BUILDING","RIVERSIDE","CA","925210001","9518275535","MPS","126400, 126500","1045","$0.00","This project focuses on the mathematical study of curved surfaces by connecting algebraic objects to them and thereby generalizing the scope of their application. One of the main notions used is that of a surface group representation, a concept which connects surfaces to generalizations of classical geometries such as Euclidean and hyperbolic geometry. The study of surfaces has surprising applications throughout many fields of mathematics and physics. Consequently, the project lies at the intersection of multiple disciplines. In addition to cutting edge mathematical research, the project will promote the progress of science and mathematics through different workshops aimed at graduate students as well as community outreach events. The educational component will also focus on creating an engaging and inclusive place for mathematical interactions for students and early career researchers.

In the past decades, both the theories of Higgs bundles and Anosov dynamics have led to significant advancements in our understanding of the geometry of surface groups. Recent breakthroughs linking these approaches are indirect and mostly involve higher rank generalizations of hyperbolic geometry known as higher rank Teichmuller spaces. The broad aim of this project is to go beyond higher rank Teichmuller spaces by using Higgs bundles to identify subvarieties of surface group representations which generalize the Fuchsian locus in quasi-Fuchsian space. The cornerstone for the approach is the role of Slodowy slices for Higgs bundles. Specifically, the PI aims to establish Anosov properties of surface group representations associated to Slodowy slices in the Higgs bundle moduli space. This approach will significantly extend applications of Higgs bundles to both Anosov representations and (G,X) geometries. It will complete the component count for moduli of surface group representations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349244","Conference: Texas Algebraic Geometry Symposium (TAGS) 2024-2026","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/01/2024","01/19/2024","Frank Sottile","TX","Texas A&M University","Continuing Grant","James Matthew Douglass","03/31/2027","$15,000.00","","sottile@tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","126400","","$0.00","The Texas Algebraic Geometry Symposium (TAGS) will be held at Texas A&M University April 5,6, and 7, 2024, and in Spring 2025 and Spring 2026. TAGS is an annual regional conference which is jointly organized by faculty at Rice University, Texas A&M University, and the University of Texas at Austin. The conference series began in 2005, and serves to enhance the educational and research environment in Texas and the surrounding states, providing an important opportunity for interaction and sharing of ideas for students and researchers in this region.

TAGS serves to ensure that members of the algebraic geometry community in the Texas region stay in regular contact and brings distinguished mathematicians and rising stars to an area with no other comparable regular gatherings in algebraic geometry. The 2024 TAGS will have nine lectures delivered by a diverse group of speakers, and will include accessible lectures for graduate students and a juried poster session for students and junior researchers. It will be held in conjunction with the annual Maxson lectures at Texas A&M the week before and delivered by Prof. David Eisenbud. The TAGS website is https://franksottile.github.io/conferences/TAGS24/index.html.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2414452","Collaborative Research: Conference: Special Trimester on Post-Quantum Algebraic Cryptography","DMS","ALGEBRA,NUMBER THEORY,AND COM, Secure &Trustworthy Cyberspace","09/01/2024","07/02/2024","Delaram Kahrobaei","NY","CUNY Queens College","Standard Grant","Tim Hodges","08/31/2025","$10,000.00","","dkahrobaei@gc.cuny.edu","6530 KISSENA BLVD","FLUSHING","NY","113671575","7189975400","MPS","126400, 806000","025Z, 7556","$0.00","This award funds participation by US-based researchers in a special trimester on Post-quantum algebraic cryptography, to be held at the The Henri Poincare Institute, Paris, France, September 9 - December 13, 2024. In recent years, there has been a substantial amount of research on quantum computers -- machines that exploit quantum mechanical phenomena to solve mathematical problems that are difficult or intractable for conventional computers. If large-scale quantum computers are ever built, they will be able to break many of the public-key cryptosystems currently in use. This would seriously compromise the confidentiality and integrity of digital communications on the Internet and elsewhere. The goal of post-quantum cryptography is to develop cryptographic systems that are secure against both quantum and classical computers, and can interoperate with existing communications protocols and networks. The thematic trimester program will bring together researchers and practitioners from academia, industry, and government institutions with diverse backgrounds to discuss quantum algorithms, quantum-safe cryptography, as well as deployment issues, from different angles.

This thematic trimester program will address various proposed cryptographic primitives that are currently considered to be quantum-safe. This includes lattice-based, multivariate, code-based, hash-based, group-based, and other primitives some of which were considered by NIST during their post-quantum standardization process. Our program will also address various functionalities of cryptographic constructions that are in high demand in real life. This includes fully homomorphic encryption that provides for private search on encrypted database and machine learning on encrypted data. Another functionality that is getting increasingly popular is outsourcing (a.k.a. delegating) computation of algebraic functions including group exponentiation, product of group exponentiations, etc., from a computationally limited client holding an input and a description of a function, to a computationally stronger entity holding a description of the same function. Further information can be found at the program website:
https://www.ihp.fr/en/events/post-quantum-algebraic-cryptography-paris

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2412921","Conference: CAAGTUS (Commutative Algebra and Algebraic Geometry in TUcSon)","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","02/14/2024","Debaditya Raychaudhury","AZ","University of Arizona","Standard Grant","Tim Hodges","04/30/2025","$15,000.00","Arvind Suresh, Zhengning Hu","draychaudhury@math.arizona.edu","845 N PARK AVE RM 538","TUCSON","AZ","85721","5206266000","MPS","126400","7556","$0.00","This award will support participation in a weekend conference to be held at the University of Arizona, Tucson on May 4 - 5. The aim of the conference is to establish a solid basis for contacts and collaborations among researchers in Commutative Algebra and Algebraic Geometry located in Arizona and its neighboring states. Its main purposes are to stimulate new directions of research, to provide opportunities to junior researchers to share their work, and to provide a venue for networking and collaboration in the southwest. Its other aim is to expand the network of algebraic and arithmetic geometers by providing an algebro-geometric complement of the Arizona Winter School.

The conference plans to host four leading researchers from Arizona and its neighboring states working in Commutative Algebra and Algebraic Geometry, who will give colloquium-style one-hour lectures on their respective areas of expertise. These hour-long lectures are expected to provide surveys of the current state of the research in these areas, and to provide suggestions for new avenues of research. There will be five or six 30-minute talks given by young researchers, as well as six to eight contributed short 20-minute talks and a poster session. Priority for these contributed talks and posters will be given to recent PhD recipients and members of groups underrepresented in mathematics. Further information is available at the conference website: https://sites.google.com/math.arizona.edu/caagtus/home

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349836","Local and Global Problems in the Relative Langlands Program","DMS","ALGEBRA,NUMBER THEORY,AND COM","08/01/2024","07/24/2024","Chen Wan","NJ","Rutgers University Newark","Standard Grant","Andrew Pollington","07/31/2027","$174,000.00","","chen.wan@rutgers.edu","123 WASHINGTON ST","NEWARK","NJ","071023026","9739720283","MPS","126400","","$0.00","This award concerns mathematical objects called reductive groups which are special kinds of topological groups characterized by abundant symmetries. These symmetries serve as key insights into understanding the intrinsic structures of objects in our universe. The study of reductive groups dates back to the late 19th century. Two crucial areas of this field are the representation theory of reductive groups and automorphic forms on reductive groups, which are specialized functions with additional symmetry on reductive groups. These two areas also have many connections to various other disciplines, including physics and computer science. This project aims to explore the restriction of representations of reductive groups to a spherical subgroup and to investigate the period integrals of automorphic forms. In the meantime, the PI will continue advising his current undergraduate and graduate students, as well as any potential students interested in studying the Langlands program. He will hold weekly meetings with them and assign suitable thesis problems. He will also continue organizing seminars and conferences in this area. Additionally, he will maintain his outreach efforts in K-12 education by mentoring high school students and coaching local kids in the Newark area for math competitions, among other activities.

To be specific, the primary objective in the local theory is to use the trace formula method to study the multiplicity problem for spherical varieties. In recent years, the PI and his collaborators have examined the local multiplicity for some spherical varieties and have proposed a conjectural multiplicity formula for all spherical varieties. Additionally, they have formulated an epsilon dichotomy conjecture for all strongly tempered spherical varieties. The PI intends to prove these conjectures and investigate further structures and properties related to multiplicity. Additionally, the PI plans to study the multiplicity for varieties that are not necessarily spherical, as well as the relations between distribution characters and orbital integrals. In the global theory, the PI intends to use the relative trace formula method and some beyond endoscopic type comparison method to study various relations between period integrals and automorphic L-functions (in particular proving the Ichino-Ikeda type formula for period integrals in some cases). Moreover, Ben-Zvi?Sakellaridis?Venkatesh have recently developed a beautiful theory of relative Langlangs duality. The PI intends to use this theory to explain all the existing automorphic integrals and to explore some new integrals. The PI also hopes to extend the theory of relative Langlands duality beyond the current spherical setting.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2337942","CAREER: Arithmetic Dynamical Systems on Projective Varieties","DMS","ALGEBRA,NUMBER THEORY,AND COM","09/01/2024","01/22/2024","Nicole Looper","IL","University of Illinois at Chicago","Continuing Grant","Tim Hodges","08/31/2029","$36,742.00","","nrlooper@uic.edu","809 S MARSHFIELD AVE M/C 551","CHICAGO","IL","606124305","3129962862","MPS","126400","1045","$0.00","This project centers on problems in a recent new area of mathematics called arithmetic dynamics. This subject synthesizes problems and techniques from the previously disparate areas of number theory and dynamical systems. Motivations for further study of this subject include the power of dynamical techniques in approaching problems in arithmetic geometry and the richness of dynamics as a source of compelling problems in arithmetic. The funding for this project will support the training of graduate students and early career researchers in arithmetic dynamics through activities such as courses and workshops, as well as collaboration between the PI and researchers in adjacent fields.

The project?s first area of focus is the setting of abelian varieties, where the PI plans to tackle various conjectures surrounding the fields of definition and S-integrality of points of small canonical height. One important component of this study is the development of quantitative lower bounds on average values of generalized Arakelov-Green?s functions, which extend prior results in the dimension one case. The PI intends to develop such results for arbitrary polarized dynamical systems, opening an avenue for a wide variety of arithmetic applications. A second area of focus concerns the relationship between Arakelov invariants on curves over number fields and one-dimensional function fields, and arithmetic on their Jacobian varieties. Here the project aims to relate the self-intersection of Zhang?s admissible relative dualizing sheaf to the arithmetic of small points on Jacobians, as well as to other salient Arakelov invariants such as the delta invariant. The third goal is to study canonical heights of subvarieties, especially in the case of divisors. A main focus here is the relationship between various measurements of the complexity of the dynamical system and the heights of certain subvarieties. The final component of the project aims to relate the aforementioned generalized Arakelov-Green?s functions to
pluripotential theory, both complex and non-archimedean.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2339274","CAREER: New directions in the study of zeros and moments of L-functions","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","02/12/2024","Alexandra Florea","CA","University of California-Irvine","Continuing Grant","Tim Hodges","06/30/2029","$87,350.00","","alexandra.m.florea@gmail.com","160 ALDRICH HALL","IRVINE","CA","926970001","9498247295","MPS","126400","1045","$0.00","This project focuses on questions in analytic number theory, and concerns properties of the Riemann zeta-function and of more general L-functions. L-functions are functions on the complex plane that often encode interesting information about arithmetic objects, such as prime numbers, class numbers, or ranks of elliptic curves. For example, the Riemann zeta-function (which is one example of an L-function) is closely connected to the question of counting the number of primes less than a large number. Understanding the analytic properties of L-functions, such as the location of their zeros or their rate of growth, often provides insight into arithmetic questions of interest. The main goal of the project is to advance the knowledge of the properties of some families of L-functions and to obtain arithmetic applications. The educational component of the project involves groups of students at different stages, ranging from high school students to beginning researchers. Among the educational activities, the PI will organize a summer school in analytic number theory focusing on young mathematicians, and will run a yearly summer camp at UCI for talented high school students.

At a more technical level, the project will investigate zeros of L-functions by studying their ratios and moments. While positive moments of L?functions are relatively well-understood, much less is known about negative moments and ratios, which have applications to many difficult questions in the field. The planned research will use insights from random matrix theory, geometry, sieve theory and analysis. The main goals fall under two themes. The first theme is developing a general framework to study negative moments of L-functions, formulating full conjectures and proving partial results about negative moments. The second theme involves proving new non-vanishing results about L-functions at special points. Values of L-functions at special points often carry important arithmetic information; the PI plans to show that wide classes of L-functions do not vanish at the central point (i.e., the center of the critical strip, where all the non-trivial zeros are conjectured to be), as well as to study correlations between the values of different L-functions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -87,8 +93,8 @@ "2347097","Collaborative Research: Conference: Texas-Oklahoma Representations and Automorphic forms (TORA)","DMS","ALGEBRA,NUMBER THEORY,AND COM","01/01/2024","12/19/2023","Melissa Emory","OK","Oklahoma State University","Standard Grant","Andrew Pollington","12/31/2026","$20,000.00","Maria Fox, Mahdi Asgari","melissa.emory@okstate.edu","401 WHITEHURST HALL","STILLWATER","OK","740781031","4057449995","MPS","126400","7556, 9150","$0.00","This award supports the TORA mathematics conference series. This series consists of annual meetings hosted by the University of North Texas, Oklahoma State University, and the University of Oklahoma on a rotating basis. This award provides support for three weekend conferences, one at the University of North Texas in Spring 2024 (TORA XIII), one at Oklahoma State University in Spring 2025 (TORA XIV), and another at the University of Oklahoma in Spring 2026 (TORA XV). Each conference will feature three prominent guest speakers from outside the Texas-Oklahoma region, in addition to other participants including students, post-doctoral researchers, and junior faculty. Regional graduate students and researchers will also give talks describing their work. These conferences will facilitate collaborations and interactions among the students and researchers in the region who work in the areas of Automorphic Forms, Representation Theory, and Number Theory.

Over the last century, the theories of automorphic forms and representations have grown enormously. Important applications impact various fields of research, ranging from number theory, coding theory, algebraic geometry, and topology to Kac-Moody algebras and quantum field theory. The interplay of automorphic forms and representation theory has been especially fruitful, and many surprising and deep results have emerged. The TORA conference series will emphasize the interplay between automorphic forms and representations, both in the classical and adelic languages, and related topics like analytic number theory and harmonic analysis.



The conference Texas-Oklahoma Representations and Automorphic forms XIII will take place on April 12-14, 2024, at the University of North Texas. Additional information can be found on the conference website: https://www.math.unt.edu/~richter/TORA/TORA13.html

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401353","Automorphic Forms and the Langlands Program","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/10/2024","Sug Woo Shin","CA","University of California-Berkeley","Continuing Grant","Andrew Pollington","06/30/2027","$87,594.00","","sug.woo.shin@berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","126400","","$0.00","This award concerns research in number theory which studies integers, prime numbers, and solutions of a system of equations over integers or rational numbers following the long tradition from ancient Greeks. In the digital age, number theory has been essential in algorithms, cryptography, and data security. Modern mathematics has seen increasingly more interactions between number theory and other areas from a unifying perspective. A primary example is the Langlands program, comprising a vast web of conjectures and open-ended questions. Even partial solutions have led to striking consequences such as verification of Fermat's Last Theorem, the Sato-Tate conjecture, the Serre conjecture, and their generalizations.

The PI's projects aim to broaden our understanding of the Langlands program and related problems in the following directions: (1) endoscopic classification for automorphic forms on classical groups, (2) a formula for the intersection cohomology of Shimura varieties with applications to the global Langlands reciprocity, (3) the non-generic part of cohomology of locally symmetric spaces, and (4) locality conjectures on the mod p Langlands correspondence. The output of research would stimulate further progress and new investigations. Graduate students will be supported on the grant to take part in these projects. The PI also plans outreach to local high schools which have large under-represented minority populations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401098","Groups and Arithmetic","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/10/2024","Michael Larsen","IN","Indiana University","Continuing Grant","Adriana Salerno","06/30/2027","$92,099.00","","larsen@math.indiana.edu","107 S INDIANA AVE","BLOOMINGTON","IN","474057000","3172783473","MPS","126400","","$0.00","This award will support the PI's research program concerning group theory and its applications. Groups specify symmetry types; for instance, all bilaterally symmetric animals share a symmetry group, which is different from that of a starfish or of a sand dollar. Important examples of groups arise from the study of symmetry in geometry and in algebra (where symmetries of number systems are captured by ``Galois groups''). Groups can often be usefully expressed as finite sequences of basic operations, like face-rotations for the Rubik's cube group, or gates acting on the state of a quantum computer. One typical problem is understanding which groups can actually arise in situations of interest. Another is understanding, for particular groups, whether all the elements of the group can be expressed efficiently in terms of a single element or by a fixed formula in terms of varying elements. The realization of a particular group as the symmetry group of n-dimensional space is a key technical method to analyze these problems. The award will also support graduate student summer research.

The project involves using character-theoretic methods alone or in combination with algebraic geometry, to solve problems about finite simple groups. In particular, these tools can be applied to investigate questions about solving equations when the variables are elements of a simple group. For instance, Thompson's Conjecture, asserting the existence, in any finite simple group of a conjugacy class whose square is the whole group, is of this type. A key to these methods is the observation that, in practice, character values are usually surprisingly small. Proving and exploiting variations on this theme is one of the main goals of the project. One class of applications is to the study of representation varieties of finitely generated groups, for instance Fuchsian groups. In a different direction, understanding which Galois groups can arise in number theory and how they can act on sets determined by polynomial equations, is an important goal of this project and, indeed, a key goal of number theorists for more than 200 years.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2401049","Conference: Representation Theory and Related Geometry","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/15/2024","04/08/2024","Laura Rider","GA","University of Georgia Research Foundation Inc","Standard Grant","James Matthew Douglass","12/31/2024","$46,000.00","Mee Seong Im","laurajoymath@gmail.com","310 E CAMPUS RD RM 409","ATHENS","GA","306021589","7065425939","MPS","126400","7556","$0.00","This is a grant to support participation in the conference ""Representation theory and related geometry: progress and prospects"" that will take place May 27-31, 2024 at the University of Georgia in Athens, GA. This conference will bring together a diverse set of participants to discuss two key areas of mathematics and their interplay. Talks will include historical perspectives on the area as well as the latest mathematical breakthroughs. A goal of the conference is to facilitate meetings between graduate students, junior mathematicians, and seasoned experts to share knowledge and inspire new avenues of research. In addition to the formally invited talks, the conference will include opportunities for contributed talks and discussion.

The interplay of representation theory and geometry is fundamental to many of the recent breakthroughs in representation theory. Topics will include the representation theory of Lie (super)algebras, and finite, algebraic, and quantum groups; cohomological methods in representation theory; modular representation theory; geometric representation theory; categorification; tensor triangular geometry and related topics in noncommutative algebraic geometry; among others. More specific topics of interest may include support varieties, cohomology and extensions, endotrivial modules, Schur algebras, tensor triangular geometry, and categorification. The conference website can be found at https://sites.google.com/view/representation-theory-geometry/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401380","Quasimaps to Nakajima Varieties","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","04/10/2024","Andrey Smirnov","NC","University of North Carolina at Chapel Hill","Continuing Grant","James Matthew Douglass","05/31/2027","$80,023.00","","asmirnov@live.unc.edu","104 AIRPORT DR STE 2200","CHAPEL HILL","NC","275995023","9199663411","MPS","126400","","$0.00","Counting curves in a given space is a fundamental problem of enumerative geometry. The origin of this problem can be traced back to quantum physics, and especially string theory, where the curve counting provides transition amplitudes for elementary particles. In this project the PI will study this problem for spaces that arise as Nakajima quiver varieties. These spaces are equipped with internal symmetries encoded in representations of quantum loop groups. Thanks to these symmetries, the enumerative geometry of Nakajima quiver varieties is extremely rich and connected with many areas of mathematics. A better understanding of the enumerative geometry of Nakajima quiver varieties will lead to new results in representation theory, algebraic geometry, number theory, combinatorics and theoretical physics. Many open questions in this field are suitable for graduate research projects and will provide ideal opportunities for students' rapid introduction to many advanced areas of contemporary mathematics.

More specifically, this project will investigate and compute the generating functions of quasimaps to Nakajima quiver varieties with various boundary conditions, uncover new dualities between these functions, and prove open conjectures inspired by 3D-mirror symmetry. The project will also reveal new arithmetic properties of the generating functions via the analysis of quantum differential equations over p-adic fields. The main technical tools to be used include the (algebraic) geometry of quasimap moduli spaces, equivariant elliptic cohomology, representation theory of quantum loop groups, and integral representations of solutions of the quantum Knizhnik-Zamolodchikov equations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2401049","Conference: Representation Theory and Related Geometry","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/15/2024","04/08/2024","Laura Rider","GA","University of Georgia Research Foundation Inc","Standard Grant","James Matthew Douglass","12/31/2024","$46,000.00","Mee Seong Im","laurajoymath@gmail.com","310 E CAMPUS RD RM 409","ATHENS","GA","306021589","7065425939","MPS","126400","7556","$0.00","This is a grant to support participation in the conference ""Representation theory and related geometry: progress and prospects"" that will take place May 27-31, 2024 at the University of Georgia in Athens, GA. This conference will bring together a diverse set of participants to discuss two key areas of mathematics and their interplay. Talks will include historical perspectives on the area as well as the latest mathematical breakthroughs. A goal of the conference is to facilitate meetings between graduate students, junior mathematicians, and seasoned experts to share knowledge and inspire new avenues of research. In addition to the formally invited talks, the conference will include opportunities for contributed talks and discussion.

The interplay of representation theory and geometry is fundamental to many of the recent breakthroughs in representation theory. Topics will include the representation theory of Lie (super)algebras, and finite, algebraic, and quantum groups; cohomological methods in representation theory; modular representation theory; geometric representation theory; categorification; tensor triangular geometry and related topics in noncommutative algebraic geometry; among others. More specific topics of interest may include support varieties, cohomology and extensions, endotrivial modules, Schur algebras, tensor triangular geometry, and categorification. The conference website can be found at https://sites.google.com/view/representation-theory-geometry/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401351","Quantum Groups, W-algebras, and Brauer-Kauffmann Categories","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","04/12/2024","Weiqiang Wang","VA","University of Virginia Main Campus","Standard Grant","James Matthew Douglass","05/31/2027","$330,000.00","","ww9c@virginia.edu","1001 EMMET ST N","CHARLOTTESVILLE","VA","229034833","4349244270","MPS","126400","","$0.00","Symmetries are patterns that repeat or stay the same when certain changes are made, like rotating a shape or reflecting it in a mirror. They are everywhere in nature, from the spirals of a seashell to the orbits of planets around the sun. They also hide behind mathematical objects and the laws of physics. Quantum groups and Lie algebras are tools mathematicians use to study these symmetries. This project is a deep dive into understanding the underlying structure of these patterns, even when they're slightly changed or twisted, and how they influence the behavior of everything around us. The project will also provide research training opportunities for graduate students.

In more detail, the PI will develop emerging directions in i-quantum groups arising from quantum symmetric pairs as well as develop applications in various settings of classical types beyond type A. The topics include braid group actions for i-quantum groups; Drinfeld presentations for affine i-quantum groups and twisted Yangians, and applications to W-algebras; character formulas in parabolic categories of modules for finite W-algebras; and categorification of i-quantum groups, and applications to Hecke, Brauer and Schur categories.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401178","Representation Theory and Symplectic Geometry Inspired by Topological Field Theory","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","04/12/2024","David Nadler","CA","University of California-Berkeley","Standard Grant","James Matthew Douglass","05/31/2027","$270,000.00","","nadler@math.berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","126400","","$0.00","Geometric representation theory and symplectic geometry are two subjects of central interest in current mathematics. They draw original inspiration from mathematical physics, often in the form of quantum field theory and specifically the study of its symmetries. This has been an historically fruitful direction guided by dualities that generalize Fourier theory. The research in this project involves a mix of pursuits, including the development of new tools and the solution of open problems. A common theme throughout is finding ways to think about intricate geometric systems in elementary combinatorial terms. The research also offers opportunities for students entering these subjects to make significant contributions by applying recent tools and exploring new approaches. Additional activities include educational and expository writing on related topics, new interactions between researchers in mathematics and physics, and continued investment in public engagement with mathematics.

The specific projects take on central challenges in supersymmetric gauge theory, specifically about phase spaces of gauge fields, their two-dimensional sigma-models, and higher structures on their branes coming from four-dimensional field theory. The main themes are the cocenter of the affine Hecke category and elliptic character sheaves, local Langlands equivalences and relative Langlands duality, and the topology of Lagrangian skeleta of Weinstein manifolds. The primary goals of the project include an identification of the cocenter of the affine Hecke category with elliptic character sheaves as an instance of automorphic gluing, the application of cyclic symmetries of Langlands parameter spaces to categorical forms of the Langlands classification, and a comparison of polarized Weinstein manifolds with arboreal spaces.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401025","Conference: Algebraic Cycles, Motives and Regulators","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","04/10/2024","Deepam Patel","IN","Purdue University","Standard Grant","Andrew Pollington","04/30/2025","$15,000.00","","patel471@purdue.edu","2550 NORTHWESTERN AVE # 1100","WEST LAFAYETTE","IN","479061332","7654941055","MPS","126400","7556","$0.00","This award is to support US participation in Regulators V, the fifth in a series of international conferences dedicated to the mathematics around the theory of regulators, that will take place June 3-13, 2024, at the University of Pisa. The Regulators conferences are an internationally recognized and well-respected series of conferences on topics surrounding the theory of Regulators, many of which have played a key role in recent breakthroughs in mathematics. The conference will bring together a diverse group of participants at a wide range of career stages, from graduate students to senior professors and provide a supportive environment for giving talks, exchanging ideas, and beginning new collaborations. This has traditionally been a fruitful place for early career researchers in these fields to connect with potential collaborators and mentors at other institutions, working on related topics. This award is mainly to support such participants.

Regulators play a central role in algebraic geometry and number theory, being the common thread relating algebraic cycles and motives to number theory and arithmetic. They are the central objects appearing in several well-known conjectures relating L-functions and algebraic cycles, including the Birch--Swinnerton-Dyer conjecture, and conjectures of Deligne, Beilinson, and Bloch-Kato relating special values of L-functions of varieties to algebraic cycles and K-theory. The study of these objects have led to the development of related fields including Iwasawa theory, K-theory, and motivic homotopy theory. They also appear in many areas of mathematics outside algebraic geometry and number theory, most notably in mathematical physics. The topics covered at Regulators V are likely to include recent developments in Iwasawa theory and p-adic L-functions, K-theory, motivic homotopy theory, motives and algebraic cycles, hodge theory, microlocal analysis in characteristic p, and special values of L-functions and additional related areas of research including applications to mathematical physics.


Additional information can be found on the conference website:
http://regulators-v.dm.unipi.it/regulators-v-web.html

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -101,10 +107,10 @@ "2401422","Algebraic Geometry and Strings","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/09/2024","Ron Donagi","PA","University of Pennsylvania","Continuing Grant","Adriana Salerno","06/30/2028","$95,400.00","","donagi@math.upenn.edu","3451 WALNUT ST STE 440A","PHILADELPHIA","PA","191046205","2158987293","MPS","126400","","$0.00","Exploration of the interactions of physical theories (string theory and quantum field theory) with mathematics (especially algebraic geometry) has been extremely productive for decades, and the power of this combination of tools and approaches only seems to strengthen with time. The goal of this project is to explore and push forward some of the major issues at the interface of algebraic geometry with string theory and quantum field theory. The research will employ and combine a variety of techniques from algebraic geometry, topology, integrable systems, String theory, and Quantum Field theory. The project also includes many broader impact activities such as steering and organization of conferences and schools, membership of international boards and prize committees, revising Penn?s graduate program, curricular development at the graduate and undergraduate level, advising postdocs, graduate and undergraduate students, editing several public service volumes and editing of journals and proceedings volumes.

More specifically, the project includes, among other topics: a QFT-inspired attack on the geometric Langlands conjecture via non-abelian Hodge theory; a mathematical investigation of physical Theories of class S in terms of variations of Hitchin systems; applications of ideas from supergeometry to higher loop calculations in string theory; exploration of moduli questions in algebraic geometry, some of them motivated by a QFT conjecture, others purely within algebraic geometry; further exploration of aspects of F theory and establishment of its mathematical foundations; and exploration of categorical symmetries and defect symmetry TFTs. Each of these specific research areas represents a major open problem in math and/or in physics, whose solution will make a major contribution to the field.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349388","Analytic Langlands Correspondence","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/09/2024","Alexander Polishchuk","OR","University of Oregon Eugene","Continuing Grant","James Matthew Douglass","06/30/2027","$82,862.00","","apolish@uoregon.edu","1776 E 13TH AVE","EUGENE","OR","974031905","5413465131","MPS","126400","","$0.00","This is a project in the field of algebraic geometry with connections to number theory and string theory. Algebraic geometry is the study of geometric objects defined by polynomial equations, and related mathematical structures. Three research projects will be undertaken. In the main project the PI will provide a generalization of the theory of automorphic forms, which is an important classical area with roots in number theory. This project provides research training opportunities for graduate students.

In more detail, the main project will contribute to the analytic Langlands correspondence for curves over local fields. The goal is to study the action of Hecke operators on a space of Schwartz densities associated with the moduli stack of bundles on curves over local fields, and to relate the associated eigenfunctions and eigenvalues to objects equipped with an action of the corresponding Galois group. As part of this project, the PI will prove results on the behavior of Schwartz densities on the stack of bundles near points corresponding to stable and very stable bundles. A second project is related to the geometry of stable supercurves. The PI will develop a rigorous foundation for integrating the superstring supermeasure of the moduli space of supercurves. The third project is motivated by the homological mirror symmetry for symmetric powers of punctured spheres: the PI will construct the actions of various mapping class groups on categories associated with toric resolutions of certain toric hypersurface singularities and will find a relation of this picture to Ozsvath-Szabo's categorical knot invariants.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401472","Spheres of Influence: Arithmetic Geometry and Chromatic Homotopy Theory","DMS","ALGEBRA,NUMBER THEORY,AND COM, GEOMETRIC ANALYSIS","09/01/2024","04/10/2024","Jared Weinstein","MA","Trustees of Boston University","Continuing Grant","Adriana Salerno","08/31/2027","$82,195.00","","jsweinst@math.bu.edu","1 SILBER WAY","BOSTON","MA","022151703","6173534365","MPS","126400, 126500","","$0.00","The principal investigator plans to build a bridge between two areas of mathematics: number theory and topology. Number theory is an ancient branch of mathematics concerned with the whole numbers and primes. Some basic results in number theory are the infinitude of primes and the formula which gives all the Pythagorean triples. Topology is the study of shapes, but one doesn't remember details like length and angles; the surfaces of a donut and a coffee mug are famously indistinguishable to a topologist. An overarching theme in topology is to invent invariants to distinguish among shapes. For instance, a pair of pants is different from a straw because ""number of holes"" is an invariant which assigns different values to them (2 and 1 respectively, but one has to be precise about what a hole is). The notion of ""hole"" can be generalized to higher dimensions: a sphere has no 1-dimensional hole, but it does have a 2-dimensional hole and even a 3-dimensional hole (known as the Hopf fibration, discovered in 1931). There are ""spheres"" in every dimension, and the determination of how many holes each one has is a major unsolved problem in topology. Lately, the topologists' methods have encroached into the domain of number theory. In particular the branch of number theory known as p-adic geometry, involving strange number systems allowing for decimal places going off infinitely far to the left, has made an appearance. The principal investigator will draw upon his expertise in p-adic geometry to make contributions to the counting-holes-in-spheres problem. He will also organize conferences and workshops with the intent of drawing together number theorists and topologists together, as currently these two realms are somewhat siloed from each other. Finally, the principal investigator plans to train his four graduate students in methods related to this project.

The device which counts the number of holes in a shape is called the ""homotopy group"". Calculating the homotopy groups of the spheres is notoriously difficult and interesting at the same time. There is a divide-and-conquer approach to doing this known as chromatic homotopy theory, which replaces the sphere with its K(n)-localized version. Here K(n) is the Morava K-theory spectrum. Work in progress by the principal investigator and collaborators has identified the homotopy groups of the K(n)-local sphere up to a torsion subgroup. The techniques used involve formal groups, p-adic geometry, and especially perfectoid spaces, which are certain fractal-like entities invented in 2012 by Fields Medalist Peter Scholze. The next step in the project is to calculate the Picard group of the K(n)-local category, using related techniques. After this, the principal investigator will turn his attention to the problem known as the ""chromatic splitting conjecture"", which has to do with iterated localizations of the sphere at different K(n). This is one of the missing pieces of the puzzle required to assemble the homotopy groups of the spheres from their K(n)-local analogues. This award is jointly supported by the Algebra and Number Theory and Geometric Analysis programs.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2401337","Algebraic Cycles and L-functions","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/03/2024","Chao Li","NY","Columbia University","Standard Grant","Adriana Salerno","06/30/2027","$230,000.00","","chaoli@math.columbia.edu","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","126400","","$0.00","The research in this project concerns one of the basic questions in mathematics: solving algebraic equations. The information of the solutions are encoded in various mathematical objects: algebraic cycles, automorphic forms and L-functions. The research will deepen the understanding of these mathematical objects and the connection between them, especially in high dimensions, which requires solving many new problems, developing new tools and interactions in diverse areas, and appealing to new perspectives which may shed new light on old problems. It will also advance the techniques for understanding the arithmetic of elliptic curves, particularly the Birch and Swinnerton-Dyer conjecture, one of the seven Millennium Prize Problems of the Clay Mathematics Institute. The PI will continue to mentor graduate students, organize conferences and workshops, and write expository articles.

The PI will work on several projects relating arithmetic geometry with automorphic L-function, centered around the common theme of the generalization and applications of the Gross--Zagier formula. The PI will investigate the Kudla--Rapoport conjecture for parahoric levels. The PI will extend the arithmetic inner product formula to orthogonal groups, and study the Bloch--Kato conjecture of symmetric power motives of elliptic curves and endoscopic cases of the arithmetic Gan--Gross--Prasad conjectures. The PI will also investigate a new arithmetic relative trace formula approach towards a Gross--Zagier type formula for orthogonal Shimura varieties.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2400550","Splicing Summation Formulae and Triple Product L-Functions","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/04/2024","Jayce Getz","NC","Duke University","Standard Grant","Andrew Pollington","06/30/2027","$220,000.00","","jgetz@math.duke.edu","2200 W MAIN ST","DURHAM","NC","277054640","9196843030","MPS","126400","","$0.00","This award concerns the Langlands program which has been described as a grand unification theory within mathematics. In some sense the atoms of the theory are automorphic representations. The Langlands functoriality conjecture predicts that a collection of natural correspondences preserve these atoms. To even formulate this conjecture precisely, mathematical subjects as diverse as number theory, representation theory, harmonic analysis, algebraic geometry, and mathematical physics are required. In turn, work on the conjecture has enriched these subjects, and in some cases completely reshaped them.

One particularly important example of a correspondence that should preserve automorphic representations is the automorphic tensor product. It has been known for some time that in order to establish this particular case of Langlands functoriality it suffices to prove that certain functions known as L-functions are analytically well-behaved. More recently, Braverman and Kazhdan, Ngo, Lafforgue and Sakellaridis have explained that the expected properties of these L-functions would follow if one could obtain certain generalized Poisson summation formulae. The PI has isolated a particular family of known Poisson summation formulae and proposes to splice them together to obtain the Poisson summation formulae relevant for establishing the automorphic tensor product.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2420166","Conference: The Mordell conjecture 100 years later","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/04/2024","Bjorn Poonen","MA","Massachusetts Institute of Technology","Standard Grant","Andrew Pollington","06/30/2025","$29,970.00","","poonen@math.mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","126400","7556","$0.00","The award will support a conference, ``The Mordell conjecture 100 years later'', at the Massachusetts Institute of Technology during the week July 8-12, 2024. The conference website, showing the list of invited speakers, is https://mordell.org/ . The Mordell conjecture, proved in 1983, is one of the landmarks of modern number theory. A conference on this topic is needed now, because in recent years, there have been advances on different aspects of the conjecture, while other key questions remain unsolved. This would be the first conference to bring together all the researchers coming from these different perspectives. The conference will feature 16 hour-long lectures, with speakers ranging from the original experts to younger mathematicians at the forefront of current research. Some lectures will feature surveys of the field, which have educational value especially for the next generation of researchers. The conference will also feature a problem session and many 5-minute lightning talk slots, which will give junior participants an opportunity to showcase their own research on a wide variety of relevant topics. The award will support the travel and lodging of a variety of mathematicians including those from underrepresented groups in mathematics and attendees from colleges and universities where other sources of funding are unavailable. Materials from the lectures, problem session, and lightning talks will be made publicly available on the website, to reach an audience broader than just conference attendees.

The Mordell conjecture motivated much of the development of arithmetic geometry in the 20th century, both before and after its resolution by Faltings. The conference will feature lectures covering a broad range of topics connected with the Mordell conjecture, its generalizations, and other work it has inspired. In particular, it will build on recent advances in the following directions: 1) nonabelian analogues of Chabauty's p-adic method; 2) the recent proof via p-adic Hodge theory; 3) uniform bounds on the number of rational points; 4) generalizations to higher-dimensional varieties, studied by various methods: analytic, cohomological, and computational.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401164","Conference: Latin American School of Algebraic Geometry","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","04/10/2024","Evgueni Tevelev","MA","University of Massachusetts Amherst","Standard Grant","Adriana Salerno","04/30/2025","$20,000.00","","tevelev@math.umass.edu","101 COMMONWEALTH AVE","AMHERST","MA","010039252","4135450698","MPS","126400","7556","$0.00","This award will provide travel support for graduate students and early career mathematicians from the United States to participate in the research school ""Latin American School of Algebraic Geometry"" that will take place in Cabo Frio, Brazil from August 12 to 23, 2024, and will be hosted by IMPA (Institute for Pure and Applied Mathematics), a renowned center for mathematical research and post-graduate education founded in 1952 and situated in Rio de Janeiro, Brazil. This will be the fifth edition of the ELGA series. The previous events were held in Buenos Aires (Argentina, 2011), Cabo Frio (Brazil, 2015), Guanajuato (Mexico, 2017), and Talca (Chile, 2019). ELGA is a major mathematical event in Latin America, a focal meeting point for the algebraic geometry community and a great opportunity for junior researchers to network and to learn from the world experts in the field. ELGA workshops are unique in their dedicated efforts to nurture the next generation of leaders in STEM in the Americas. The travel support for U.S. participants from the National Science Foundation will further strengthen the ties between the universities and promote scientific cooperation between future mathematicians in Latin America and the U.S. The website of the conference is https://impa.br/en_US/eventos-do-impa/2024-2/v-latin-american-school-of-algebraic-geometry-and-applications-v-elga/

Algebraic geometry has long enjoyed a central role in mathematics by providing a precise language to describe geometric shapes called algebraic varieties, with applications ranging from configuration spaces in physics to parametric models in statistics. This versatile language is used throughout algebra and has fueled multiple recent advances, not only in algebraic geometry itself but also in representation theory, number theory, symplectic geometry, and other fields. Over the course of two weeks, courses by Cinzia Casagrande (University of Torino, Italy), Charles Favre (École Polytechnique, France), Joaquin Moraga (UCLA, USA), Giancarlo Urzúa (Catholic University, Chile), and Susanna Zimmermann (University of Paris-Saclay, France) will cover a wide range of topics including geometry of Fano manifolds, singularities of algebraic varieties, Cremona groups of projective varieties, Higgs bundles, and geometry of moduli spaces. Each course will include two hours of tutorial sessions coordinated by the course lecturers with the assistance of advanced graduate students participating in the research workshop. Additional talks and presentations by a combination of senior and junior researchers are intended to give a panoramic view of algebraic geometry and its applications.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2401337","Algebraic Cycles and L-functions","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/03/2024","Chao Li","NY","Columbia University","Standard Grant","Adriana Salerno","06/30/2027","$230,000.00","","chaoli@math.columbia.edu","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","126400","","$0.00","The research in this project concerns one of the basic questions in mathematics: solving algebraic equations. The information of the solutions are encoded in various mathematical objects: algebraic cycles, automorphic forms and L-functions. The research will deepen the understanding of these mathematical objects and the connection between them, especially in high dimensions, which requires solving many new problems, developing new tools and interactions in diverse areas, and appealing to new perspectives which may shed new light on old problems. It will also advance the techniques for understanding the arithmetic of elliptic curves, particularly the Birch and Swinnerton-Dyer conjecture, one of the seven Millennium Prize Problems of the Clay Mathematics Institute. The PI will continue to mentor graduate students, organize conferences and workshops, and write expository articles.

The PI will work on several projects relating arithmetic geometry with automorphic L-function, centered around the common theme of the generalization and applications of the Gross--Zagier formula. The PI will investigate the Kudla--Rapoport conjecture for parahoric levels. The PI will extend the arithmetic inner product formula to orthogonal groups, and study the Bloch--Kato conjecture of symmetric power motives of elliptic curves and endoscopic cases of the arithmetic Gan--Gross--Prasad conjectures. The PI will also investigate a new arithmetic relative trace formula approach towards a Gross--Zagier type formula for orthogonal Shimura varieties.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401464","Conference: Solvable Lattice Models, Number Theory and Combinatorics","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","04/09/2024","Solomon Friedberg","MA","Boston College","Standard Grant","James Matthew Douglass","05/31/2025","$22,500.00","","friedber@bc.edu","140 COMMONWEALTH AVE","CHESTNUT HILL","MA","024673800","6175528000","MPS","126400","7556","$0.00","This award supports the participation of US-based researchers in the Conference on Solvable Lattice Models, Number Theory and Combinatorics that will take place June 24-26, 2024 at the Hamilton Mathematics Institute at Trinity College Dublin. Solvable lattice models first arose in the description of phase change in physics and have become useful tools in mathematics as well. In the past few years a group of researchers have found that they may be used to effectively model quantities arising in number theory and algebraic combinatorics. At the same time, other scholars have used different methods coming from representation theory to investigate these quantities. This conference will be a venue to feature these developments and to bring together researchers working on related questions using different methods and students interested in learning more about them.

This conference focuses on new and emerging connections between solvable lattice models and special functions on p-adic groups and covering groups, uses of quantum groups, Hecke algebras and other methods to study representations of p-adic groups and their covers, and advances in algebraic combinatorics and algebraic geometry. Spherical and Iwahori Whittaker functions are examples of such special functions and play an important role in many areas. The website for this conference is https://sites.google.com/bc.edu/solomon-friedberg/dublin2024.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401114","Parahoric Character Sheaves and Representations of p-Adic Groups","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/09/2024","Charlotte Chan","MI","Regents of the University of Michigan - Ann Arbor","Continuing Grant","James Matthew Douglass","06/30/2027","$105,981.00","","charchan@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","126400","","$0.00","In the past half century, cutting-edge discoveries in mathematics have occurred at the interface of three major disciplines: number theory (the study of prime numbers), representation theory (the study of symmetries using linear algebra), and geometry (the study of solution sets of polynomial equations). The interactions between these subjects has been particularly influential in the context of the Langlands program, arguably the most expansive single project in modern mathematical research. The proposed research aims to further these advances by exploring geometric techniques in representation theory, especially motivated by questions within the context of the Langlands conjectures. This project also provides research training opportunities for undergraduate and graduate students.

In more detail, reductive algebraic groups over local fields (local groups) and their representations control the behavior of symmetries in the Langlands program. This project aims to develop connections between representations of local groups and two fundamental geometric constructions: Deligne-Lusztig varieties and character sheaves. Over the past decade, parahoric analogues of these geometric objects have been constructed and studied, leading to connections between (conjectural) algebraic constructions of the local Langlands correspondence to geometric phenomena, and thereby translating open algebraic questions to tractable problems in algebraic geometry. In this project, the PI will wield these novel positive-depth parahoric analogues of Deligne-Lusztig varieties and character sheaves to attack outstanding conjectures in the local Langlands program.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2411537","Conference: Comparative Prime Number Theory Symposium","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","04/05/2024","Wanlin Li","MO","Washington University","Standard Grant","Adriana Salerno","04/30/2025","$10,000.00","","wanlin@wustl.edu","ONE BROOKINGS DR","SAINT LOUIS","MO","63110","3147474134","MPS","126400","7556","$0.00","The workshop Comparative Prime Number Theory Symposium, which is the first scientific event to focus predominantly on this subject, will take place on the UBC--Vancouver campus from June 17--21, 2024. One of the first and central topics in the research of number theory is to study the distribution of prime numbers. In 1853, Chebyshev observed that there seems to be more primes taking the form of a multiple of four plus three than a multiple of four plus one. This phenomenon is now referred to as Chebyshev's bias and its study led to a new branch of number theory, comparative prime number theory. As a subfield of analytic number theory, research in this area focuses on examining how prime counting functions and other arithmetic functions compare to one another. This field has witnessed significant growth and activity in the last three decades, especially after the publication of the influential article on Chebyshev's bias by Rubinstein and Sarnak in 1994. The primary goal of this award will be to provide participant support and fund US-based early career researchers to attend this unique event, giving them the opportunity to discuss new ideas, advance research projects, and interact with established researchers.

The symposium will bring together many leading and early-career researchers with expertise and interest in comparative prime number theory to present and discuss various aspects of current research in the field, with special emphasis on results pertaining to the distribution of counting functions in number theory and zeros of L-functions, consequences of quantitative Linear Independence, oscillations of the Mertens sum, and the frequency of sign changes. Through this symposium, we will advertise the recently disseminated survey ""An Annotated Bibliography for Comparative Prime Number Theory"" by Martin et al which aims to record every publication within the topic of comparative prime number theory, together with a summary of results, and presenting a unified system of notation and terminology for referring to the quantities and hypotheses that are the main objects of study. Another important outcome of the symposium will be compiling and publicizing a problem list, with the hope of stimulating future research and providing young researchers with potential projects. Information about the conference can be found at the website: https://sites.google.com/view/crgl-functions/comparative-prime-number-theory-symposium

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -112,10 +118,10 @@ "2334874","Conference: Pittsburgh Links among Analysis and Number Theory (PLANT)","DMS","ALGEBRA,NUMBER THEORY,AND COM, ANALYSIS PROGRAM","02/01/2024","01/19/2024","Carl Wang Erickson","PA","University of Pittsburgh","Standard Grant","James Matthew Douglass","01/31/2025","$20,000.00","Theresa Anderson, Armin Schikorra","carl.wang-erickson@pitt.edu","4200 FIFTH AVENUE","PITTSBURGH","PA","152600001","4126247400","MPS","126400, 128100","7556","$0.00","This award will support the four-day conference ""Pittsburgh Links among Analysis and Number Theory (PLANT)"" that will take place March 4-7, 2024 in Pittsburgh, PA. The purpose of the conference is to bring together representatives of two disciplines with a shared interface: number theory and analysis. There is a large potential for deeper collaboration between these fields resulting in new and transformative mathematical perspectives, and this conference aims at fostering such an interchange. In particular, the conference is designed to attract PhD students and post-doctoral scholars into working on innovations at this interface.

To encourage the development of new ideas, the conference speakers, collectively, represent many subfields that have developed their own distinctive blend of analysis and number theory, such as analytic number theory, arithmetic statistics, analytic theory of modular and automorphic forms, additive combinatorics, discrete harmonic analysis, and decoupling. While there have been a wide variety of conferences featuring these subfields in relative isolation, the PIs are excited at PLANT's potential for sparking links among all of these subfields and giving early-career participants the opportunity to be part of this exchange. The conference website is https://sites.google.com/view/plant24/home.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401041","Conference: Singularities in Ann Arbor","DMS","ALGEBRA,NUMBER THEORY,AND COM","05/01/2024","03/28/2024","Mircea Mustata","MI","Regents of the University of Michigan - Ann Arbor","Standard Grant","Adriana Salerno","04/30/2025","$33,758.00","Qianyu Chen","mmustata@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","126400","7556","$0.00","The conference ""Singularities in Ann Arbor"", scheduled for May 13-17, 2024, at the University of Michigan, Ann Arbor, will explore recent progress in the study of singularities in algebraic geometry. Algebraic geometry, in simple terms, concerns itself with studying geometric objects defined by polynomial equations. This conference will focus on several recent advances concerning singularities: these are points where the geometric objects behave in unexpected ways (such as the bumps or dents on a normally flat surface). Understanding these singularities not only satisfies intellectual curiosity but also plays a crucial role in classifying and comprehending global complex geometric structures. More details about the conference, as well as the list of confirmed lecturers, are available on the conference website, at https://sites.google.com/view/singularitiesinaa.

The conference will feature four lecture series presented by leading experts and rising stars in the field, covering recent advancement related to singularities. These lectures will introduce fresh perspectives and tools, including Hodge Theory, D-modules, and symplectic topology, to address challenging questions in algebraic geometry. The conference aims to make these complex ideas accessible to a younger audience, fostering engagement and understanding among participants. Additionally, the conference will provide a platform for young researchers to showcase their work through a poster session, encouraging collaboration and discussion among participants. This award will provide travel and lodging support for about 35 early-career conference participants.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2344680","Conference: Tensor Invariants in Geometry and Complexity Theory","DMS","ALGEBRA,NUMBER THEORY,AND COM, GEOMETRIC ANALYSIS, Algorithmic Foundations","03/15/2024","02/20/2024","Luke Oeding","AL","Auburn University","Standard Grant","James Matthew Douglass","02/28/2025","$40,000.00","","oeding@auburn.edu","321-A INGRAM HALL","AUBURN","AL","368490001","3348444438","MPS","126400, 126500, 779600","7556, 9150","$0.00","The conference Tensor Invariants in Geometry and Complexity Theory will take place May 13-17, 2024 at Auburn University. This conference aims to bring together early-career researchers and experts to study tensor invariants, their appearance in pure algebraic and differential geometry, and their application in Algebraic Complexity Theory and Quantum Information. The workshop will feature talks from both seasoned experts and promising young researchers. The event is designed to facilitate new research connections and to initiate new collaborations. The conference will expose the participants to state-of-the-art research results that touch a variety of scientific disciplines. The activities will support further development of both pure mathematics and the ""down-stream"" applications in each area of scientific focus (Algebraic and Differential Geometry, Algebraic Complexity, Quantum Information).

The conference is centered on invariants in geometry, divided into three themes: Algebraic and Differential Geometry, Tensors and Complexity, and Quantum Computing and Quantum Information. Geometry has long been a cornerstone of mathematics, and invariants are the linchpins. Regarding Algebraic and Differential Geometry, the organizers are inviting expert speakers on topics such as the connections between projective and differential geometry. Considerations in these areas, such as questions about dimensions and defining equations of secant varieties, have led to powerful tools both within geometry and applications in areas such as computational complexity and quantum information. Likewise, the organizers are inviting application-area experts in Algebraic Complexity and Quantum Information. This natural juxtaposition of pure and applied mathematics will lead to new and interesting connections and help initiate new research collaborations. In addition to daily talks by seasoned experts, the conference will include young researchers in a Poster Session and provide networking opportunities, including working group activities, to help early career researchers meet others in the field, which will provide opportunities for new (and ongoing) research collaborations. It is anticipated that these collaborations will continue long after the meeting is over. The conference webpage is: https://webhome.auburn.edu/~lao0004/jmlConference.html.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2342225","RTG: Numbers, Geometry, and Symmetry at Berkeley","DMS","ALGEBRA,NUMBER THEORY,AND COM, WORKFORCE IN THE MATHEMAT SCI","08/01/2024","03/18/2024","Tony Feng","CA","University of California-Berkeley","Continuing Grant","Andrew Pollington","07/31/2029","$1,196,058.00","Martin Olsson, David Nadler, Sug Woo Shin, Yunqing Tang","fengt@berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","126400, 733500","","$0.00","The project will involve a variety of activities organized around the research groups in number theory, geometry, and representation theory at UC Berkeley. These subjects study the structure and symmetries of mathematical equations, and have applications to (for example) cryptography, codes, signal processing, and physics. There will be an emphasis on training graduate students to contribute to society as scientists, educators, and mentors.

More precisely, RTG will be used to organize annual graduate research workshops, with external experts, as well as weekly research seminars to keep up-to-date on cutting-edge developments. Summer programs on Research Experiences of Undergraduates will provide valuable research exposure to undergraduates, and also mentorship training to graduate students. Postdocs will be hired to help lead these activities. Finally, the project will fund outreach to local schools. At the core of all these activities is the goal of training students and postdocs as strong workforce in their dual roles as mentors and mentees, recruiting students into the ?eld with a good representation of underrepresented groups, and providing a setting for collaboration between all levels and across di?erent areas.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2402436","Conference: Visions in Arithmetic and Beyond","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","03/26/2024","Akshay Venkatesh","NJ","Institute For Advanced Study","Standard Grant","Andrew Pollington","05/31/2025","$44,975.00","Alexander Gamburd","akshay@math.ias.edu","1 EINSTEIN DR","PRINCETON","NJ","085404952","6097348000","MPS","126400","7556","$0.00","This award provides funding to help defray the expenses of participants in the conference ""Visions in Arithmetic and Beyond"" (conference website https://www.ias.edu/math/events/visions-in-arithmetic-and-beyond ) to be held at the Institute for Advanced Study and Princeton University from June 3 to June 7, 2024. Those speaking at the meeting include the leading researchers across arithmetic, analysis and geometry.

The conference will provide high-level talks by mathematicians who are both outstanding researchers and excellent speakers. These will synthesize and expose a broad range of recent advances in number theory as well as related developments in analysis and dynamics. In addition to the talks by leading researchers there is also time allotted for a session on the best practices for mentoring graduate students and postdocs.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401152","Conference: Modular forms, L-functions, and Eigenvarieties","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/01/2024","03/26/2024","John Bergdall","AR","University of Arkansas","Standard Grant","Adriana Salerno","11/30/2024","$15,000.00","","bergdall@uark.edu","1125 W MAPLE ST STE 316","FAYETTEVILLE","AR","727013124","4795753845","MPS","126400","7556, 9150","$0.00","This award supports US-based scientists to attend the conference ""Modular Forms, L-functions, and Eigenvarieties"". The event will take place in Paris, France from June 18, 2024, until June 21, 2024. Whole numbers are the atoms of our mathematical universe. Number theorists study why patterns arise among whole numbers. In the 1970's, Robert Langlands proposed connections between number theory and mathematical symmetry. His ideas revolutionized the field. Some of the most fruitful approaches to his ideas have come via calculus on geometric spaces. The conference funded here will expose cutting edge research on such approaches. The ideas disseminated at the conference will have a broad impact on the field. The presentations of leading figures will propel junior researchers toward new theories. The US-based participants will make a written summary of the conference. The summaries will encourage the next generation to adopt the newest perspectives. Writing them will also engender a spirit of collaboration within the research community. The summaries along with details of the events will be available on the website https://www.eventcreate.com/e/bellaiche/.

The detailed aim of the conference is exposing research on modular forms and L-functions in the context of eigenvarieties. An eigenvariety is a p-adic space that encodes congruence phenomena in number theory. Families of eigenforms, L-functions, and other arithmetic objects find their homes on eigenvarieties. The conference's primary goal is exposing the latest research on such families. The presentations will place new research and its applications all together in one place, under the umbrella of the p-adic Langlands program.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2341365","Conference: Southern Regional Number Theory Conference","DMS","ALGEBRA,NUMBER THEORY,AND COM","02/01/2024","01/19/2024","Gene Kopp","LA","Louisiana State University","Standard Grant","James Matthew Douglass","01/31/2026","$35,000.00","Fang-Ting Tu","gkopp@lsu.edu","202 HIMES HALL","BATON ROUGE","LA","708030001","2255782760","MPS","126400","9150","$0.00","Southern Regional Number Theory Conferences (SRNTCs) are planned to be held in the Gulf Coast region March 9?11, 2024, and in Spring 2025, at Louisiana State University in Baton Rouge. The 2024 conference will be the 10th anniversary of the conference series. The SRNTC series serves as an annual number theory event for the Gulf Coast region. It brings together researchers from the region and beyond to disseminate and discuss fundamental research in various branches of number theory, in turn fostering communication and collaboration between researchers. Local students and early-career researchers attending the conferences are exposed to a wide array of problems and techniques, including specialized topics that may have no local experts at their home institutions. Students and early-career researchers are given opportunities to present their research through contributed talks and to expand their professional network.

SRNTC 2024 will feature about ten invited talks by established experts from four countries, speaking on topics in algebraic number theory, analytic number theory, and automorphic forms. It will also feature about twenty-five contributed talks, mostly by regional graduate students and early-career researchers. Information about SRNTC 2024 and SRNTC 2025, including a registration form and the schedule for each conference, is available at the conference website (https://www.math.lsu.edu/srntc).

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2342225","RTG: Numbers, Geometry, and Symmetry at Berkeley","DMS","ALGEBRA,NUMBER THEORY,AND COM, WORKFORCE IN THE MATHEMAT SCI","08/01/2024","03/18/2024","Tony Feng","CA","University of California-Berkeley","Continuing Grant","Andrew Pollington","07/31/2029","$1,196,058.00","Martin Olsson, David Nadler, Sug Woo Shin, Yunqing Tang","fengt@berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","126400, 733500","","$0.00","The project will involve a variety of activities organized around the research groups in number theory, geometry, and representation theory at UC Berkeley. These subjects study the structure and symmetries of mathematical equations, and have applications to (for example) cryptography, codes, signal processing, and physics. There will be an emphasis on training graduate students to contribute to society as scientists, educators, and mentors.

More precisely, RTG will be used to organize annual graduate research workshops, with external experts, as well as weekly research seminars to keep up-to-date on cutting-edge developments. Summer programs on Research Experiences of Undergraduates will provide valuable research exposure to undergraduates, and also mentorship training to graduate students. Postdocs will be hired to help lead these activities. Finally, the project will fund outreach to local schools. At the core of all these activities is the goal of training students and postdocs as strong workforce in their dual roles as mentors and mentees, recruiting students into the ?eld with a good representation of underrepresented groups, and providing a setting for collaboration between all levels and across di?erent areas.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2333970","Conference: Collaborative Workshop in Algebraic Geometry","DMS","ALGEBRA,NUMBER THEORY,AND COM","06/01/2024","03/21/2024","Sarah Frei","NH","Dartmouth College","Standard Grant","Andrew Pollington","05/31/2025","$24,400.00","Ursula Whitcher, Rohini Ramadas, Julie Rana","sarah.frei@dartmouth.edu","7 LEBANON ST","HANOVER","NH","037552170","6036463007","MPS","126400","7556, 9150","$0.00","This award supports participants to attend a collaborative algebraic geometry research workshop at the Institute for Advanced Study (IAS) during the week of June 24-28, 2024. The goals of the workshop are to facilitate significant research in algebraic geometry and to strengthen the community of individuals in the field from underrepresented backgrounds. We will place a particular focus on forming connections across different career stages. Participants will join project groups composed of a leader and co-leader together with two to three junior participants and will spend the workshop engaged in focused and substantive research.

The projects to be initiated during this workshop represent a wide range of subfields of algebraic geometry (e.g. intersection theory, toric geometry and arithmetic geometry), as well as connections to other fields of math (e.g. representation theory). Specifically, topics include: abelian covers of varieties, del Pezzo surfaces over finite fields, positivity of toric vector bundles, Chow rings of Hurwitz spaces with marked ramification, Ceresa cycles of low genus curves, and the geometry of Springer fibers and Hessenberg varieties. More information is available at https://sites.google.com/view/wiag2024/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349888","Conference: International Conference on L-functions and Automorphic Forms","DMS","ALGEBRA,NUMBER THEORY,AND COM","04/01/2024","03/15/2024","Larry Rolen","TN","Vanderbilt University","Standard Grant","Adriana Salerno","03/31/2025","$25,000.00","Jesse Thorner, Andreas Mono","larry.rolen@vanderbilt.edu","110 21ST AVE S","NASHVILLE","TN","372032416","6153222631","MPS","126400","7556","$0.00","This award provides support for the conference entitled ""International Conference on L-functions and Automorphic Forms'', which will take place at Vanderbilt University in Nashville, Tennessee on May 13--16 2024. This is part of an annual series hosted by Vanderbilt, known as the Shanks conference series. The main theme will be on new developments and recent interactions between the areas indicated in the title. The interplay between automorphic forms and L-functions has a long and very fruitful history in number theory, and bridging both fields is still a very active area of research. This conference is oriented at establishing and furthering dialogue on new developments at the boundary of these areas. This will foster collaboration between researchers working in these fields.

One beautiful feature of modern number theory is that many problems of broad interest, in areas of study as diverse as arithmetic geometry to mathematical physics, can be solved in an essentially optimal way if the natural extension of the Riemann hypothesis holds for L-functions associated to automorphic representations. Although many generalizations and applications around L-functions have have already been worked out, there are still various fundamental open problems among them to tackle, including bounds for and the value distribution of L-functions. The former is related to the pursuit of so-called sub-convexity bounds for L-functions. The latter is related to the Birch and Swinnterton-Dyer conjecture (another ?Millenium problem? posed by the Clay Mathematics institute). These pursuits are closely connected with the Langlands program, a ?grand unifying theory? relating automorphic forms. Further details can be found on the conference website https://my.vanderbilt.edu/shanksseries/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401305","Conference: ANTS XVI: Algorithmic Number Theory Symposium 2024","DMS","ALGEBRA,NUMBER THEORY,AND COM, Secure &Trustworthy Cyberspace","07/01/2024","02/27/2024","Andrew Sutherland","MA","Massachusetts Institute of Technology","Standard Grant","Andrew Pollington","06/30/2025","$36,000.00","","drew@math.mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","126400, 806000","7556","$0.00","This award provides funds for early-career researchers (graduate students, postdocs, and tenure-track faculty not having other NSF support) to attend the sixteenth edition of the Algorithmic Number Theory Symposium (ANTS-XVI) held July 15-19, 2024 at the Massachusetts Institute of Technology (MIT). The ANTS meetings, held biannually since 1994, are the premier international forum for new research in computational number theory. As an established conference series, ANTS attracts invited and contributed lectures of the highest quality, and serves as a forum for dissemination of new ideas and techniques throughout the research community in the area of computational number theory and number-theoretic aspects of cryptography. In addition to numerous applications to theoretical mathematics, these fields have immense importance through real world connections to computer security.

The ANTS meetings are devoted to algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic number theory, geometry of numbers, arithmetic algebraic geometry, modular forms, finite fields, and applications of number theory to cryptography. Participants include academic researchers in both mathematics and computer science, as well as mathematicians in industry who work on cryptography and other areas of application; similarly, the topics presented include both pure and applied topics. The review process for contributed lectures and the subsequent production of a proceedings volume provides documentation of the presented results at a quality level comparable to an international research journal in mathematics. This award funds lodging and US-based travel for researchers who might not otherwise be able to participate in this premier event. Funding priority will be given to those contributing papers or posters; the organizers also seek to actively promote participation by women and underrepresented minorities.

More information about the conference can be found at https://antsmath.org/ANTSXVI/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." diff --git a/Analysis/Awards-Analysis-2024.csv b/Analysis/Awards-Analysis-2024.csv index bebf18b..9950a07 100644 --- a/Analysis/Awards-Analysis-2024.csv +++ b/Analysis/Awards-Analysis-2024.csv @@ -1,10 +1,11 @@ "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract" +"2400329","RUI: Fourier Restriction and Fourier Dimension for Fractals","DMS","ANALYSIS PROGRAM","09/01/2024","08/20/2024","Kyle Hambrook","CA","San Jose State University Foundation","Standard Grant","Wing Suet Li","08/31/2027","$150,000.00","","kyle.hambrook@sjsu.edu","210 N 4TH ST FL 4","SAN JOSE","CA","951125569","4089241400","MPS","128100","9229","$0.00","Many objects in nature are self-similar, that is, they display similar features when examined at different scales. Examples include the shapes of river channels, snowflakes, ferns, and lightning, just to name a few. In mathematics, these self-similar objects are characterized as ?fractals.? Fractals appear in the study of paths of particle motion, branching biological structures, crystals, turbulence, cloud formation, and other areas. The Fourier transform is a mathematical operation ubiquitous in signal and image processing, spectroscopy, quantum mechanics, and many other fields of science and engineering. The overarching theme of this research project is the study of the connections between the (geometric and arithmetic) structure of fractal sets and the Fourier transforms of functions and measures defined on such sets. The work will be done in collaboration with undergraduate and graduate students, in keeping with the goal of the PI to help recruit and train future mathematicians and other STEM professionals.


The PI will solve problems in the construction of fractal Salem sets (i.e., sets whose Hausdorff and Fourier dimensions are equal), calculation of the exact Fourier dimension of fractal sets, optimality of Fourier restriction on fractals, and construction of measures with rapid Fourier decay on various fractal sets (including fractal subsets of curves and surfaces, sets of badly approximable vectors, and sums and products of fractal sets). To solve these problems, the PI will extend techniques he has developed over the decade in solving related problems. Progress will feedback into other areas of analysis by providing insight to researchers working on problems in geometric measure theory, additive combinatorics, and partial differential equations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2339565","CAREER: Brown Measure and non-Hermitian Random Matrices","DMS","OFFICE OF MULTIDISCIPLINARY AC, PROBABILITY, ANALYSIS PROGRAM","09/15/2024","07/31/2024","Ping Zhong","WY","University of Wyoming","Continuing Grant","Jan Cameron","08/31/2029","$254,771.00","","pzhong.uh@gmail.com","1000 E UNIVERSITY AVE","LARAMIE","WY","820712000","3077665320","MPS","125300, 126300, 128100","1045, 9150, 9251","$0.00","This CAREER award supports a five-year project in free probability, random matrix theory, and their applications. Free probability began as a subfield of the theory of von Neumann algebras, which in turn originated in a series of papers by Murray and von Neumann in the 1930s, as part of an effort to provide mathematical foundations for quantum mechanics. A key concept in free probability is the notion of free independence, which generalizes the classical notion of independence of random variables, enabling the development of a robust ?noncommutative probability theory? in the setting of von Neumann algebras, where rich mathematical structure emerges from the interactions of objects known as free random variables (owing in part to the fact that their multiplication, like that of matrices of complex numbers, is not commutative). Methods from free probability are now a cornerstone of the structure theory of certain von Neumann algebras, and have applications to a variety of other fields, including random matrix theory and quantum information theory. In this project, the PI will study several important open problems on probability distributions of free random variables and explore their applications to random matrix models. The project integrates research with education and will provide research opportunities for both graduate and undergraduate students, complemented by outreach initiatives to teach and mentor middle school and high school students, with a particular emphasis on supporting students from underrepresented backgrounds.

The Brown measure of a free random variable is analogous to the eigenvalue counting measure of a square matrix. It is an extension of spectral measures of normal operators to non-normal operators. This measure encodes a great deal of information and can predict the limiting distributions of non-Hermitian random matrix models. In this project, the PI seeks to develop analytic techniques for computing the Brown measures of a diverse range of free random variables, motivated by operator algebras, random matrix theory, and high-dimensional statistics. The boundary values of certain operator-valued subordination functions will be explored using tools in complex analysis, operator algebras, and noncommutative analysis. The project will investigate random variables formed through addition, multiplication, or polynomials of free random variables. The new Brown measure results will then be used to analyze limiting laws and the convergence of non-Hermitian random matrix models.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2426785","Conference: Midwestern Workshop on Asymptotic Analysis 2024","DMS","ANALYSIS PROGRAM","09/01/2024","08/15/2024","Norman Levenberg","IN","Indiana University","Standard Grant","Marian Bocea","08/31/2025","$23,039.00","","nlevenbe@indiana.edu","107 S INDIANA AVE","BLOOMINGTON","IN","474057000","3172783473","MPS","128100","7556","$0.00","This award supports participants in the 2024 Midwestern Workshop on Asymptotic Analysis, scheduled to take place in October 2024 at Indiana University. The goal of the conference is to disseminate research advances and to foster cooperation among researchers working in various areas of analysis and partial differential equations, particularly from colleges and universities in the midwest. Special emphasis is placed on attracting graduate students, both as participants and as speakers, to encourage the professional development of early-career scholars in various areas of mathematical analysis with both academic and industry applications.

Major research themes to be addressed during the meeting include approximation theory, functional analysis, harmonic analysis, mathematical physics, potential theory and several complex variables. The event starts with a Friday afternoon colloquium talk by a senior researcher, and continues on Saturday and Sunday with an additional ten talks by researchers working in the above fields. All of the Saturday and Sunday talks will be given by early career researchers, including junior faculty, postdocs, and graduate students. The conference will also feature a poster session where other beginning researchers in analysis can publicize their work.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350543","NSF-BSF: Semigroup Operator Algebras - Representations, Boundaries and Dynamics","DMS","OFFICE OF MULTIDISCIPLINARY AC, ANALYSIS PROGRAM","09/01/2024","08/13/2024","Boyu Li","NM","New Mexico State University","Standard Grant","Jan Cameron","08/31/2027","$254,546.00","","boyuli@nmsu.edu","1050 STEWART ST.","LAS CRUCES","NM","88003","5756461590","MPS","125300, 128100","014Z, 9150","$0.00","This project seeks to advance understanding of semigroups within the framework of operator algebras, an area of mathematical analysis. The mathematical field of operator algebras originated in the pioneering work of Murray and von Neumann in the 1930s to develop mathematical foundations for quantum mechanics and has grown into a vital subarea of modern analysis, with connections to many other mathematical fields, including geometry, topology, mathematical physics, and algebra. Operator algebras and the theory of semigroups have enjoyed a fruitful dialogue since the 1990s. Semigroups are algebraic structures in which (like the real numbers) elements can be combined using algebraic operations, but which (unlike the real numbers) generally lack inverse operations. Due to this algebraic structure, semigroups are often useful in modeling ?irreversible? phenomena, such as the time evolution of some physical systems, and have proven to be an essential tool across the mathematical sciences. This project will develop new theories and methods to study semigroups and their associated operator algebras through their representations, boundaries and dynamics. The project will also foster international collaboration, enhance the research culture at New Mexico State University, and provide training of graduate and undergraduate students with an emphasis on including students from underrepresented groups. This is a project funded jointly by the National Science Foundation?s Division of Mathematical Sciences, in the Directorate for Mathematical and Physical Sciences (NSF-MPS-DMS), and the Israel Binational Science Foundation (BSF) in accordance with the Memorandum of Understanding between the NSF and the BSF.

This project concerns the interrelationships among several classes of semigroup representations and associated operator algebras and dynamics. Unlike groups whose representations are always unitary, semigroups have richer classes of representations as operators on Hilbert spaces. The first goal of this project is to develop a general theory of dilation of isometric covariant representations to characterize boundary representations, and thereby calculate the C*-envelope of universal non-self-adjoint semigroup operator algebras. The focus is on the class of non-Nica-amenable semigroups, whose representations remain highly mysterious. The second goal of this project is to study semigroups from a dynamical perspective, seeking to understand the properties of semigroup operator algebras from the properties of the underlying dynamics. In particular, this project aims to build a general framework to study two-sided semigroup actions, which is motivated by mathematical physics. This project will also investigate the dynamics of self-similar actions, which exhibits new phenomena that generalize many group dynamics. Finally, this project will investigate the representation theory of Artin semigroups, which is a rich class of semigroups with deep connections to various areas of mathematics. In addition to providing concrete examples, the study of Artin semigroups will also contribute to multivariable operator theory and non-commutative geometry.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349959","Concrete K-theory operations for topological physics","DMS","OFFICE OF MULTIDISCIPLINARY AC, ANALYSIS PROGRAM","09/01/2024","08/01/2024","Terry Loring","NM","University of New Mexico","Standard Grant","Jan Cameron","08/31/2027","$210,548.00","","loring@math.unm.edu","1700 LOMAS BLVD NE STE 2200","ALBUQUERQUE","NM","87131","5052774186","MPS","125300, 128100","9150","$0.00","Detecting and measuring the stability of waves, be they sound waves, wave patterns of electrons or light, is a critical task in modern physics. Specifically, stable waves, bound to a position, are a central topic in the study of quantum materials. Low-power transistors and small lasers are some of the devices that can be designed from quantum materials. The critical mathematical tool for detecting these stable waves is called K-theory, a topic that cuts across many of the main subject areas of mathematics. Using tools from operator algebras, a subfield of mathematical analysis, a form of K-theory has recently been discovered to be useful in the development of mathematical probes of computer models of materials. Loring?s group will be developing the subject of K-theory for operator algebras, with particular emphasis on new mathematical techniques that can be implemented in software used by physicists. This project will also create opportunities for students at the University of New Mexico and Florida A&M University to do research and participate in internships at Sandia National Laboratories.


The mathematics to be developed in this project will focus on multivariable spectrum for noncommuting operators and associated invariants in real and complex K-theory. These invariants can be applied to detect local topology in a variety of quantum materials. These invariants depend on a local gap in the Hamiltonian, a concept that can be made precise using the Clifford spectrum of the various position operators and the Hamiltonian. Local gaps can exist in topological metals, and in composite systems where a metal lead abuts a topological insulator. The fundamental challenge is to find invariants for matrix models of locally gapped free-fermion systems. Using unsuspended E-theory as a model for real and complex K-homology, Loring will develop simple formulas for these invariants and determine if these invariants are complete.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349828","Spatial restriction of exponential sums to thin sets and beyond","DMS","ANALYSIS PROGRAM","06/01/2024","04/01/2024","Ciprian Demeter","IN","Indiana University","Standard Grant","Wing Suet Li","05/31/2027","$299,999.00","","demeterc@indiana.edu","107 S INDIANA AVE","BLOOMINGTON","IN","474057000","3172783473","MPS","128100","","$0.00","In recent years, the PI has developed a new tool called decoupling that measures the extent to which waves traveling in different directions interact with each other. While this tool was initially intended to analyze differential equations that describe wave cancellations, it has also led to important breakthroughs in number theory. For example, Diophantine equations are potentially complicated systems of equations involving whole numbers. They are used to generate scrambling and diffusion keys, which are instrumental in encrypting data. Mathematicians are interested in counting the number of solutions to such systems. Unlike waves, numbers do not oscillate, at least not in an obvious manner. But we can think of numbers as frequencies and thus associate them with waves. In this way, problems related to counting the number of solutions to Diophantine systems can be rephrased in the language of quantifying wave interferences. This was the case with PI's breakthrough resolution of the Main Conjecture in Vinogradov's Mean Value Theorem. The PI plans to further extend the scope of decoupling toward the resolution of fundamental problems in harmonic analysis, geometric measure theory, and number theory. He will seek to make the new tools accessible and useful to a large part of the mathematical community. This project provides research training opportunities for graduate students.


Part of this project is aimed at developing the methodology to analyze the Schrödinger maximal function in the periodic setting. Building on his recent progress, the PI aims to incorporate Fourier analysis and more delicate number theory into the existing combinatorial framework. Decouplings have proved successful in addressing a wide range of problems in such diverse areas as number theory, partial differential equations, and harmonic analysis. The current project seeks to further expand the applicability of this method in new directions. One of them is concerned with finding sharp estimates for the Fourier transforms of fractal measures supported on curved manifolds. The PI seeks to combine decoupling with sharp estimates for incidences between balls and tubes. In yet another direction, he plans to further investigate the newly introduced tight decoupling phenomenon. This has deep connections to both number theory and the Lambda(p) estimates.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2424018","CAREER: Oscillatory Integrals and the Geometry of Projections","DMS","ANALYSIS PROGRAM","04/15/2024","04/24/2024","Hong Wang","NY","New York University","Continuing Grant","Marian Bocea","08/31/2028","$163,054.00","","hongwang@math.ucla.edu","70 WASHINGTON SQ S","NEW YORK","NY","100121019","2129982121","MPS","128100","1045","$0.00","This project involves research at the interface of Fourier analysis and geometric measure theory. Fourier analysis studies the relation between a function and its Fourier transform. The Fourier transform of a function, in rough terms, represents the function via a superposition of frequencies. Geometric measure theory studies the geometric properties of sets and measures under transformations. Fractal sets, or sets with highly irregular geometry, are of particular interest in this regard. Recently, the connection between Fourier analysis and geometric measure theory has led to substantial progress in both fields. This project explores the interaction between these two fields, along with possible applications to other fields such as dynamics and number theory. The project also supports workshops for graduate students and early-career mathematicians: these events will promote mathematical expertise within the indicated research areas, will contribute to the professional training of participants, and will foster new research collaborations.

The project combines work in restriction theory (within Fourier analysis) and the theory of projections (within geometric measure theory). One component of the planned research involves the study of the mass of a function, with Fourier transform supported on the sphere, on a fractal set. Another component investigates the dimensions of fractal sets under certain linear or nonlinear maps parametrized by curved manifolds. A final component concerns the Kakeya conjecture, which asks how large must a set be if it contains a unit line segment in every direction. These three components, while distinct, are highly interrelated, and progress in each area is anticipated to inform ongoing work in all of these areas.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2339565","CAREER: Brown Measure and non-Hermitian Random Matrices","DMS","OFFICE OF MULTIDISCIPLINARY AC, PROBABILITY, ANALYSIS PROGRAM","09/15/2024","07/31/2024","Ping Zhong","WY","University of Wyoming","Continuing Grant","Jan Cameron","08/31/2029","$254,771.00","","pzhong@uwyo.edu","1000 E UNIVERSITY AVE","LARAMIE","WY","820712000","3077665320","MPS","125300, 126300, 128100","1045, 9150, 9251","$0.00","This CAREER award supports a five-year project in free probability, random matrix theory, and their applications. Free probability began as a subfield of the theory of von Neumann algebras, which in turn originated in a series of papers by Murray and von Neumann in the 1930s, as part of an effort to provide mathematical foundations for quantum mechanics. A key concept in free probability is the notion of free independence, which generalizes the classical notion of independence of random variables, enabling the development of a robust ?noncommutative probability theory? in the setting of von Neumann algebras, where rich mathematical structure emerges from the interactions of objects known as free random variables (owing in part to the fact that their multiplication, like that of matrices of complex numbers, is not commutative). Methods from free probability are now a cornerstone of the structure theory of certain von Neumann algebras, and have applications to a variety of other fields, including random matrix theory and quantum information theory. In this project, the PI will study several important open problems on probability distributions of free random variables and explore their applications to random matrix models. The project integrates research with education and will provide research opportunities for both graduate and undergraduate students, complemented by outreach initiatives to teach and mentor middle school and high school students, with a particular emphasis on supporting students from underrepresented backgrounds.

The Brown measure of a free random variable is analogous to the eigenvalue counting measure of a square matrix. It is an extension of spectral measures of normal operators to non-normal operators. This measure encodes a great deal of information and can predict the limiting distributions of non-Hermitian random matrix models. In this project, the PI seeks to develop analytic techniques for computing the Brown measures of a diverse range of free random variables, motivated by operator algebras, random matrix theory, and high-dimensional statistics. The boundary values of certain operator-valued subordination functions will be explored using tools in complex analysis, operator algebras, and noncommutative analysis. The project will investigate random variables formed through addition, multiplication, or polynomials of free random variables. The new Brown measure results will then be used to analyze limiting laws and the convergence of non-Hermitian random matrix models.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348715","Differentiability in Carnot Groups and Metric Measure Spaces","DMS","ANALYSIS PROGRAM","09/01/2024","07/17/2024","Gareth Speight","OH","University of Cincinnati Main Campus","Standard Grant","Marian Bocea","08/31/2027","$263,078.00","","gareth.speight@uc.edu","2600 CLIFTON AVE","CINCINNATI","OH","452202872","5135564358","MPS","128100","5918, 5920, 5935, 5946, 5952","$0.00","A function is considered to be smooth or differentiable if at every point it is has a derivative, or in other words, a well-defined rate of change. Many familiar functions are smooth, and smoothness properties are convenient and prevalent in scientific applications. However, non-smooth functions also frequently arise in mathematics and its applications, such as optimization. This project concerns differentiability phenomena in non-smooth environments. Specifically, it seeks to understand when non-smooth objects possess hidden smoothness structures. While non-smooth objects are more difficult to understand, they are often equipped with additional structure that is not initially visible. For instance, Lipschitz functions (i.e., those functions which expand distances by at most a multiplicative factor) are differentiable at most points of their domain. The project investigates these and related phenomena, it seeks to describe when a partially defined function can be extended to a smooth function, and explores when a function can be approximated by a smooth function. The project will promote research collaboration and will generate research training opportunities for both graduate and undergraduate students.

The project centers on two broad topics of research. First, the PI seeks a deeper understanding of the Whitney extension and Lusin approximation questions for mappings between Carnot groups. A significant complication, not present in the Euclidean case, is that the maps to be constructed must satisfy nonlinear constraints reflecting the underlying geometry of these non-Euclidean environments. A second line of study investigates the differentiability properties of Lipschitz functions in Euclidean spaces, Carnot groups, and metric or Banach spaces. A fundamental theorem due to Rademacher states that every Lipschitz function defined in a Euclidean domain is differentiable almost everywhere. However, in many situations one in fact finds differentiability points inside measure zero sets. This observation led to the modern study of sets of universal differentiability. The project seeks to test the limits of Rademacher?s theorem through an improved understanding of universal differentiability sets, via the use of maximal directional derivatives and other methods.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349865","Analysis and Dynamics in Several Complex Variables","DMS","ANALYSIS PROGRAM","06/01/2024","03/21/2024","Xianghong Gong","WI","University of Wisconsin-Madison","Standard Grant","Marian Bocea","05/31/2027","$333,182.00","","gong@math.wisc.edu","21 N PARK ST STE 6301","MADISON","WI","537151218","6082623822","MPS","128100","","$0.00","This award supports research at the interface of several complex variables, differential geometry, and dynamical systems. Complex analysis studies the behavior and regularity of functions defined on and taking values in spaces of complex numbers. It remains an indispensable tool across many domains in the sciences, engineering, and economics. This project considers the smoothness of transformations on a domain defined by complex valued functions when the domain is deformed. Using integral formulas, the PI will study how invariants of a domain vary when the underlying structure of the domain changes. Another component of the project involves the study of resonance. The PI will use small divisors that measure non-resonance to classify singularities of the complex structure arising in linear approximations of curved manifolds. The project will involve collaboration with researchers in an early career stage and will support the training of graduate students.

Motivated by recent counterexamples showing that smooth families of domains may be equivalent by a discontinuous family of biholomorphisms, the PI will study the existence of families of biholomorphisms between families of domains using biholomorphism groups and other analytic tools such as Bergman metrics. The PI will construct a global homotopy formula with good estimates for suitable domains in a complex manifold. One of the goals is to construct a global formula in cases when a local homotopy formula fails to exist. The PI will use such global homotopy formulas to investigate the stability of holomorphic embeddings of domains with strongly pseudoconvex or concave boundary in a complex manifold, when the complex structure on the domains is deformed. The PI will use this approach to investigate stability of global Cauchy-Riemann structures on Cauchy-Riemann manifolds of higher codimension. The project seeks a holomorphic classification of neighborhoods of embeddings of a compact complex manifold in complex manifolds via the Levi-form and curvature of the normal bundle. In addition, the PI will study the classification of Cauchy-Riemann singularities for real manifolds using methods from several complex variables and small-divisor conditions in dynamical systems.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2421914","Collaborative Research: Conference: Prairie Analysis Seminar 2024-2025","DMS","ANALYSIS PROGRAM","09/15/2024","07/19/2024","Virginia Naibo","KS","Kansas State University","Standard Grant","Marian Bocea","08/31/2026","$25,855.00","Diego Maldonado","vnaibo@ksu.edu","1601 VATTIER STREET","MANHATTAN","KS","665062504","7855326804","MPS","128100","7556, 9150","$0.00","This award supports participants at the 2024 and 2025 editions of the Prairie Analysis Seminar. The Fall 2024 event will be held in October 2024 at the University of Kansas; the Fall 2025 event will be hosted by Kansas State University (date to be determined). The Prairie Analysis Seminar is an ongoing collaboration between the mathematics departments at Kansas State University and the University of Kansas. Since its inception in 2001, the conference has showcased the research of a diverse group of mathematicians working in analysis and partial differential equations. The event provides participants in early career stages with the opportunity to present their work via contributed talks, to get advice from experts, and to expand their professional networks. In addition, the event promotes the participation of underrepresented and underserved groups in mathematics, in particular, researchers from smaller colleges and universities in geographical proximity to the host institutions.

Invited speakers at the Prairie Analysis Seminar are leading scholars well known for their contributions to active areas of research within analysis and partial differential equations and for their ability to communicate with a broad mathematical audience. Each event features an invited principal speaker, who gives two one-hour lectures, accompanied by two invited speakers who each give a one-hour lecture. An important component of the seminar is the time reserved for short talks by early career participants, including advanced Ph.D. students and postdocs. The conference also includes a session for discussion of open problems suggested by conference participants.

https://www.math.ksu.edu/research/centers-groups/group/analysis/prairie_seminar.html

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -31,9 +32,9 @@ "2400115","Collaborative Research: Conference: Brazos Analysis Seminar","DMS","ANALYSIS PROGRAM","04/01/2024","03/25/2024","Kate Juschenko","TX","University of Texas at Austin","Standard Grant","Wing Suet Li","03/31/2027","$16,000.00","","kate.juschenko@gmail.com","110 INNER CAMPUS DR","AUSTIN","TX","787121139","5124716424","MPS","128100","7556","$0.00","This award provides three years of funding to help defray the expenses of participants in the semi-annual conference series ""Brazos Analysis Seminar"" 2024-2026, the first meeting of which will be held in Spring 2024 at Texas Christian University. Subsequent meetings will rotate among the University of Texas at Austin, University of Houston, Texas A&M University, and Baylor University. The Brazos Analysis Seminar will bring together analysts at academic institutions within the South-Central region of the United States on a regular basis to communicate their research, with a particular emphasis on providing an opportunity for young researchers and graduate students to meet, collaborate and disseminate their work on a regular basis during the academic year. The format for the seminar provides ample opportunity for graduate students, postdocs, and junior investigators to present their work, start new collaborations, learn about the latest developments in modern analysis, and to advance their careers.

The scientific topics of this conference series will focus on the analytic theory of operator algebras and operator space theories and their connections to harmonic analysis, ergodic theory, dynamic systems, and the quantum information theory. These include free probability method in the study of quantum groups, Fourier multipliers theory on noncommutative Lp spaces, dynamical system, and K-theory of C*-algebras and von Neumann algebras. In each meeting, there will be 3 plenary talks given by prominent experts and 6 contributed talks presented by 3 experts from the region, and 3 postdoctoral or upper level PhD students. The goal is to keep both junior and senior researchers in the south-central institutions exposed and informed of the latest major mathematical developments in noncommutative Analysis, and to enhance and advance the research on the related topics. Additional information is available on the seminar website https://sites.google.com/site/brazosanalysisseminar.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2400112","Collaborative Research: Conference: Brazos Analysis Seminar","DMS","ANALYSIS PROGRAM","04/01/2024","03/25/2024","Zhizhang Xie","TX","Texas A&M University","Standard Grant","Wing Suet Li","03/31/2027","$16,400.00","","xie@math.tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","128100","7556","$0.00","This award provides three years of funding to help defray the expenses of participants in the semi-annual conference series ""Brazos Analysis Seminar"" 2024-2026, the first meeting of which will be held in Spring 2024 at Texas Christian University. Subsequent meetings will rotate among the University of Texas at Austin, University of Houston, Texas A&M University, and Baylor University. The Brazos Analysis Seminar will bring together analysts at academic institutions within the South-Central region of the United States on a regular basis to communicate their research, with a particular emphasis on providing an opportunity for young researchers and graduate students to meet, collaborate and disseminate their work on a regular basis during the academic year. The format for the seminar provides ample opportunity for graduate students, postdocs, and junior investigators to present their work, start new collaborations, learn about the latest developments in modern analysis, and to advance their careers.

The scientific topics of this conference series will focus on the analytic theory of operator algebras and operator space theories and their connections to harmonic analysis, ergodic theory, dynamic systems, and the quantum information theory. These include free probability method in the study of quantum groups, Fourier multipliers theory on noncommutative Lp spaces, dynamical system, and K-theory of C*-algebras and von Neumann algebras. In each meeting, there will be 3 plenary talks given by prominent experts and 6 contributed talks presented by 3 experts from the region, and 3 postdoctoral or upper level PhD students. The goal is to keep both junior and senior researchers in the south-central institutions exposed and informed of the latest major mathematical developments in noncommutative Analysis, and to enhance and advance the research on the related topics. Additional information is available on the seminar website https://sites.google.com/site/brazosanalysisseminar.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2400111","Collaborative Research: Conference: Brazos Analysis Seminar","DMS","ANALYSIS PROGRAM","04/01/2024","03/25/2024","Mehrdad Kalantar","TX","University of Houston","Standard Grant","Wing Suet Li","03/31/2027","$16,000.00","","kalantar@math.uh.edu","4300 MARTIN LUTHER KING BLVD","HOUSTON","TX","772043067","7137435773","MPS","128100","7556","$0.00","This award provides three years of funding to help defray the expenses of participants in the semi-annual conference series ""Brazos Analysis Seminar"" 2024-2026, the first meeting of which will be held in Spring 2024 at Texas Christian University. Subsequent meetings will rotate among the University of Texas at Austin, University of Houston, Texas A&M University, and Baylor University. The Brazos Analysis Seminar will bring together analysts at academic institutions within the South-Central region of the United States on a regular basis to communicate their research, with a particular emphasis on providing an opportunity for young researchers and graduate students to meet, collaborate and disseminate their work on a regular basis during the academic year. The format for the seminar provides ample opportunity for graduate students, postdocs, and junior investigators to present their work, start new collaborations, learn about the latest developments in modern analysis, and to advance their careers.

The scientific topics of this conference series will focus on the analytic theory of operator algebras and operator space theories and their connections to harmonic analysis, ergodic theory, dynamic systems, and the quantum information theory. These include free probability method in the study of quantum groups, Fourier multipliers theory on noncommutative Lp spaces, dynamical system, and K-theory of C*-algebras and von Neumann algebras. In each meeting, there will be 3 plenary talks given by prominent experts and 6 contributed talks presented by 3 experts from the region, and 3 postdoctoral or upper level PhD students. The goal is to keep both junior and senior researchers in the south-central institutions exposed and informed of the latest major mathematical developments in noncommutative Analysis, and to enhance and advance the research on the related topics. Additional information is available on the seminar website https://sites.google.com/site/brazosanalysisseminar.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2402022","Conference: Dynamical Systems and Fractal Geometry","DMS","ANALYSIS PROGRAM","04/15/2024","04/03/2024","Pieter Allaart","TX","University of North Texas","Standard Grant","Jan Cameron","03/31/2025","$32,017.00","Kiko Kawamura, Kirill Lazebnik","allaart@unt.edu","1112 DALLAS DR STE 4000","DENTON","TX","762051132","9405653940","MPS","128100","7556","$0.00","This award provides support for participants to attend the conference ?Dynamical Systems and Fractal Geometry? to be held at the University of North Texas from May 14-17, 2024. The primary goal of the conference is to foster interaction and collaboration between researchers in several fields of mathematics: fractal geometry, complex dynamics, thermodynamic formalism, random dynamical systems, and open dynamical systems. These fields are interrelated through both the methods used and in the fundamental questions of their study. The conference will bring together mathematicians from these fields ranging from senior experts to graduate students; experts will give standard 45?50-minute plenary lectures, and students will have the opportunity to give 5-10 minute ?lightning talks?. The conference will also include a career panel. More information on the conference, including a list of speakers, can be found on the conference website: https://pcallaart3.wixsite.com/conference.

The fields represented in this conference have broad motivations and applications in several classical areas of mathematics and physics beyond dynamical systems and geometry, including number theory, probability theory, and statistical mechanics. Thermodynamic formalism is a framework for unifying many aspects of these fields, and its investigation triggers research and collaboration on the problem of the existence and uniqueness of equilibrium states of the various systems studied in these fields. Limit sets of conformal dynamical systems, and in particular Julia sets arising in complex dynamics, are typically of a fractal nature and understanding their fine fractal properties such as Hausdorff, packing, Assouad and Fourier dimensions provides a true challenge for fractal geometers. The conference aims to advance research in these directions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349322","Banach Spaces: Theory and Applications","DMS","ANALYSIS PROGRAM","07/01/2024","06/20/2024","Thomas Schlumprecht","TX","Texas A&M University","Standard Grant","Wing Suet Li","06/30/2027","$257,986.00","","t-schlumprecht@tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","128100","","$0.00","Logistics planning, including optimal distribution of products, leads to questions about maps with weighted distances, and routes that minimize these distances. Transportation cost spaces, also known as Lipschitz-free spaces, Wasserstein spaces, Arens-Eals spaces, and Earthmover spaces, have been used to model such problems. They can be viewed as a framework to study nonlinear metric spaces by embedding them isometrically and linearly densely into Banach spaces and provide powerful tools to study the nonlinear geometry of Banach spaces using well-known linear techniques for nonlinear problems. These spaces play a fundamental role in many areas of applied mathematics, engineering, physics, computer science, finance, and social sciences. Finding an optimal embedding is known to be a computationally hard problem and it has become a central problem in computer science to find low distortion embeddings. Using methods from the structure theory of Banach spaces and computational graph theory, the investigator?s goal is to achieve more precise estimates of these embeddings. He will obtain a deeper understanding of the structure of these spaces, which will result in several applications to the areas mentioned above. The principal investigator plans to organize conferences as well as mentor Ph.D. students as a part of this project.

A crucial connection exists between the L1-distortion of Transportation Cost Spaces and stochastic embeddings of the underlying metric space into trees. The investigator will further study this connection to obtain lower and upper estimations on the distortion. The second part of the project represents a contribution to Lindenstrauss?s program in determining Banach spaces that are primary, and that cannot be decomposed into essentially different subspaces. The investigator will continue to determine primary function spaces. This project concentrates on studying the primarity and related factorization properties of function spaces in two parameters, combining methods from Functional and Harmonic Analysis and Probability Theory.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2340465","CAREER: Gauge-theoretic Floer invariants, C* algebras, and applications of analysis to topology","DMS","TOPOLOGY, ANALYSIS PROGRAM","09/01/2024","02/02/2024","Sherry Gong","TX","Texas A&M University","Continuing Grant","Qun Li","08/31/2029","$89,003.00","","sgongli@tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","126700, 128100","1045","$0.00","The main research goal of this project is to apply analytic tools coming from physics, such as gauge theory and operator algebras, to topology, which is the study of geometric shapes. This research is divided into two themes: low dimensional topology and operator K-theory. In both fields, the aforementioned analytic tools are used to build invariants to study the geometric structure of manifolds, which are spaces modelled on Euclidean spaces, like the 3-dimensional space we live in. In both low dimensional topology and operator K-theory, the PI will use analytic tools to study questions about these spaces, such as how they are curved or how objects can be embedded inside them. These questions have a wide range of applications in biology and physics. The educational and outreach goals of this project involve math and general STEM enrichment programs at the middle and high school levels, with a focus on programs aimed at students from underserved communities and underrepresented groups, as well as mentorship in research at the high school, undergraduate and graduate levels.

In low dimensional topology, this project focuses on furthering our understanding of instanton and monopole Floer homologies and their relation to Khovanov homology, and using this to study existence questions of families of metrics with positive scalar curvature on manifolds, as well as questions about knot concordance. Separately this project also involves computationally studying knot concordance, both by a computer search for concordances and by computationally studying certain local equivalence and almost local equivalence groups that receive homomorphisms from the knot concordance groups. In operator algebras, this project focuses on studying their K-theory and its applications to invariants in geometry and topology. The K-theory groups of operator algebras are the targets of index maps of elliptic operators and have important applications to the geometry and topology of manifolds. This project involves studying the K-theory of certain C*-algebras and using them to study infinite dimensional spaces; studying the noncommutative geometry of groups that act on these infinite dimensional spaces and, in particular, the strong Novikov conjecture for these groups; and studying the coarse Baum-Connes conjecture for high dimensional expanders.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2402022","Conference: Dynamical Systems and Fractal Geometry","DMS","ANALYSIS PROGRAM","04/15/2024","04/03/2024","Pieter Allaart","TX","University of North Texas","Standard Grant","Jan Cameron","03/31/2025","$32,017.00","Kiko Kawamura, Kirill Lazebnik","allaart@unt.edu","1112 DALLAS DR STE 4000","DENTON","TX","762051132","9405653940","MPS","128100","7556","$0.00","This award provides support for participants to attend the conference ?Dynamical Systems and Fractal Geometry? to be held at the University of North Texas from May 14-17, 2024. The primary goal of the conference is to foster interaction and collaboration between researchers in several fields of mathematics: fractal geometry, complex dynamics, thermodynamic formalism, random dynamical systems, and open dynamical systems. These fields are interrelated through both the methods used and in the fundamental questions of their study. The conference will bring together mathematicians from these fields ranging from senior experts to graduate students; experts will give standard 45?50-minute plenary lectures, and students will have the opportunity to give 5-10 minute ?lightning talks?. The conference will also include a career panel. More information on the conference, including a list of speakers, can be found on the conference website: https://pcallaart3.wixsite.com/conference.

The fields represented in this conference have broad motivations and applications in several classical areas of mathematics and physics beyond dynamical systems and geometry, including number theory, probability theory, and statistical mechanics. Thermodynamic formalism is a framework for unifying many aspects of these fields, and its investigation triggers research and collaboration on the problem of the existence and uniqueness of equilibrium states of the various systems studied in these fields. Limit sets of conformal dynamical systems, and in particular Julia sets arising in complex dynamics, are typically of a fractal nature and understanding their fine fractal properties such as Hausdorff, packing, Assouad and Fourier dimensions provides a true challenge for fractal geometers. The conference aims to advance research in these directions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348305","Viscosity Solutions: Beyond the Wellposedness Theory","DMS","ANALYSIS PROGRAM","09/01/2024","07/26/2024","Hung Tran","WI","University of Wisconsin-Madison","Continuing Grant","Marian Bocea","08/31/2027","$100,972.00","","hung@math.wisc.edu","21 N PARK ST STE 6301","MADISON","WI","537151218","6082623822","MPS","128100","","$0.00","This project studies some nonlinear partial differential equations (PDE) that appear naturally in chemistry, physics, and engineering and which arise, for example, in the study of crystal growth, combustion, coagulation-fragmentation processes, game theory, and optimal control theory. These equations have connections with a host of other areas of mathematics, including the calculus of variations, differential games, dynamical systems, geometry, homogenization theory, and probability. The main goal of the project is to discover new underlying principles and general methods to understand the properties of solutions of the PDE under investigation. A key object of the research is a crystal growth model in which the crystal grows in both the horizontal direction, by adatoms, and the vertical direction, by dislocations or nucleation in a supersaturated media. To make practical use of the model, it is important to understand the qualitative and quantitative aspects of the growth speed and the shape of the crystal. The mentoring of graduate students in research is an important educational component of the project.

The work of the project involves two themes. The first is about critical Coagulation-Fragmentation equations and their connections with Hamilton-Jacobi equations. The Principal Investigator (PI) is interested in regularity and large-time behavior results for Hamilton-Jacobi equations which give implications on the existence of mass-conserving solutions of Coagulation-Fragmentation equations and their behavior. The second involves level-set mean curvature flow equations with driving and source terms and applications in crystal growths and turbulent combustions. The focus is on the regularity, the large-time average, and the large-time behavior of the solutions. The PI and his collaborators have recently developed new approaches which led to solutions to several open problems in these and related areas. The new approaches are expected to be developed further in this project, thereby bringing fresh perspectives on and insights into the study of nonlinear PDE and viscosity solutions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350252","Regular and Singular Incompressible Fluid Flows","DMS","ANALYSIS PROGRAM","08/01/2024","07/26/2024","Camillo De Lellis","NJ","Princeton University","Standard Grant","Marian Bocea","07/31/2027","$300,000.00","","camillo.delellis@math.ias.edu","1 NASSAU HALL","PRINCETON","NJ","085442001","6092583090","MPS","128100","","$0.00","A variety of systems in natural sciences are described through physically measurable quantities which depend on each other. For instance, we routinely measure the pressure and the temperature of the air in the Earth?s atmosphere, and such measurements depend upon the time and the location of the device used. Several fundamental laws discovered by scientists during the last three centuries give relations among the rates of change of such physical quantities and the resulting mathematical objects, called partial differential equations, are therefore ubiquitous in modern science and engineering. The partial differential equations describing the motion of incompressible, viscous and ideal fluids date back to the seventeenth and eighteenth centuries. Nonetheless, a rigorous mathematical understanding of many properties of their solutions is still lacking and some reverberates in a poor understanding of certain fundamental phenomena. A pivotal example is the apparent incompatibility of the classical mathematical treatment of these equations with the basic observation in the theory of fully developed turbulence that, in the limit of the viscosity of the fluid tending to zero, turbulent flows dissipate kinetic energy. In fact, regular solutions of the equations describing the zero-viscosity limit can be proved to conserve the kinetic energy and are therefore at odds with the latter phenomenon. Starting from the latter problem as a pivotal one, this project aims to advance our understanding of other basic properties of solutions, such as regularity, uniqueness, and stability. The project provides research training opportunities for graduate students and supports the engagement of the principal investigator in popularizing mathematics to the general public.

The project investigates two fundamental questions in incompressible fluid dynamics. The first goal is to find rigorous examples of the so-called ""zero law of fully developed turbulence"", namely the presence of anomalous dissipation in the zero-viscosity limit. The ideal solution of the latter problem is to give a proof of existence of a sequence of solutions to the incompressible Navier-Stokes equations with vanishing viscosity for which the dissipation rate of kinetic energy stays positive in the limit, without the introduction of spurious oscillations in the initial data. The second is the investigation of blow-up scenarios for smooth solutions of the Navier-Stokes and Euler equations. Both problems are formidable, and they have defied the efforts of mathematicians for decades. Given the size of the challenge, some effort will be dedicated to the investigation of simpler situations. An important example in the case of anomalous dissipation is the effect of forcing terms in the equations. An example in the case of the blow-up problem is understanding suitable deformations of the Navier-Stokes equations which embeds them in a higher parameter family of equations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349919","Ergodic Schrödinger Operators","DMS","ANALYSIS PROGRAM","08/01/2024","07/24/2024","David Damanik","TX","William Marsh Rice University","Standard Grant","Marian Bocea","07/31/2027","$291,253.00","","damanik@rice.edu","6100 MAIN ST","Houston","TX","770051827","7133484820","MPS","128100","7203","$0.00","This project aims to improve the understanding of how the amount of disorder present in an environment can promote or suppress transport in a system. This issue is studied in the context of quantum mechanics at the atomic level. Applications of new insights about quantum systems include the development of quantum computing devices and quantum algorithms. The project supports education and diversity though the mentoring of postdoctoral scholars, the training of graduate students, and the supervision of undergraduate research.

This project addresses the general theory of Schrödinger operators with ergodic potentials. These operators are relevant in many areas, primarily in quantum mechanics and approximation theory. The objective is to establish results for general base transformations and for large classes of sampling functions. The methods employed range from functional analysis via harmonic analysis to dynamical systems and ergodic theory. The investigator seeks to identify the almost sure spectral type of an ergodic family of Schrödinger operators, while establishing a version of Simon's Wonderland Theorem in this setting and answering a question of Walters about the existence of non-uniform cocycles as byproducts, to develop further gap labelling theory based on the Schwartzman group, along with a comparison with gap labelling based on K-theory, to study the Laplacian on Penrose and other aperiodically ordered tilings, and to obtain proofs of Cantor spectra via cocycle perturbation techniques beyond the two-dimensional time-discrete setting.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." diff --git a/Applied-Mathematics/Awards-Applied-Mathematics-2024.csv b/Applied-Mathematics/Awards-Applied-Mathematics-2024.csv index ba76188..47a0fb2 100644 --- a/Applied-Mathematics/Awards-Applied-Mathematics-2024.csv +++ b/Applied-Mathematics/Awards-Applied-Mathematics-2024.csv @@ -1,9 +1,11 @@ "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract" +"2407293","Geometric Problems in Elasticity of Thin Films, Kirigami, and the Monge-Ampere System","DMS","APPLIED MATHEMATICS","08/01/2024","07/24/2024","Marta Lewicka","PA","University of Pittsburgh","Standard Grant","Dmitry Golovaty","07/31/2027","$266,696.00","","lewicka@pitt.edu","4200 FIFTH AVENUE","PITTSBURGH","PA","152600001","4126247400","MPS","126600","","$0.00","The investigator pursues projects that combine questions in mathematical analysis, differential geometry, calculus of variations, materials science and engineering design. The key components are: (i) seeking to determine mechanical theories of thin multi-dimensional films with nonzero stored energy due to shape-formation processes such as growth or plasticity; (ii) the quest for regularity of solutions to a class of partial differential equations arising when the aforementioned prestrained films deform in order to release their energies; (iii) describing properties of ?kirigamized? sheets, namely thin films with cuts of different geometries and distributions. Some of these projects are accessible to graduate students and contribute to their training.

The related analytical projects include: (i) dimension reduction in nonlinear elasticity of prestrained materials, in function of the general prestrain given by a Riemannian metric, Gamma-convergence and rigidity estimates; (ii) convex integration and flexibility in the Holder regularity classes for the Monge-Ampere system and the k-Hessian system; and (iii) investigating structure and rectifiablity of geodesics in the kirigamized sheets in relation to the sheet?s deployment trajectory.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2406941","Collaborative Research: Emerging Applications of Self-Similarity in Dynamical Networks","DMS","APPLIED MATHEMATICS","08/15/2024","08/15/2024","Georgi Medvedev","PA","Drexel University","Standard Grant","Stacey Levine","07/31/2027","$170,814.00","","medvedev@drexel.edu","3141 CHESTNUT ST","PHILADELPHIA","PA","191042875","2158956342","MPS","126600","","$0.00","Networks of various kinds and scales arise across biological, social, and physical systems. Moreover, self-similarity manifests in real-world networks in multiple ways, from the hierarchical self-similarity of the Internet, to the fractal-like structure of dendritic trees of neurons and protein interaction networks, and to the multiscale organization of social and epidemiological networks. Mathematical modeling helps to understand the principles underlying network dynamics, which can be used for effective prediction and control of real-world networks. This research studies the implications of self-similar structure of networks on their emergent dynamics. It aims to bridge analytical theories of fractals and differential equations on fractals with applications in network science. A combination of techniques from the analysis on fractals and dynamical systems will be used to develop new tools for the analysis, prediction, and control of self-similar network dynamics. Graduate and undergraduate students will be trained and contribute to these research activities.

The principal investigators will develop a set of model problems aimed at elucidating dynamics of self-similar networks. They will consider the Kuramoto model of coupled phase oscillators on graphs approximating the Sierpinski Gasket and other fractals and analyze them using a combination of analytical and numerical techniques. The goal of the first project is to develop a geometric approach to the construction of harmonic maps from post-critically finite fractals to a circle. The outcomes of this project will be used to construct stable steady states of coupled oscillator models on graphs approximating these fractals. The second project is focused on synchronization and bifurcations in self-similar networks. The third project studies epidemiological networks based on an SIR (Susceptible-Infected-Removed) model on graphs approximating fractals. Combined these projects are expected to deliver a new set of tools for studying interacting dynamical systems on self-similar sets.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2408264","Analysis of Nonlinear Partial Differential Equations including Boundary Value problems in Kinetic Theory, Free Boundary Fluid Dynamics, and the Einstein-Boltzmann system","DMS","APPLIED MATHEMATICS","08/15/2024","08/13/2024","Robert Strain","PA","University of Pennsylvania","Standard Grant","Hailiang Liu","07/31/2027","$300,000.00","","strain@math.upenn.edu","3451 WALNUT ST STE 440A","PHILADELPHIA","PA","191046205","2158987293","MPS","126600","","$0.00","This project aims to advance the mathematical analysis of non-linear partial differential equations used in a wide range of applications. The first part of this project involves the study of fluid dynamics problems with free boundaries, aimed at enhancing the understanding of water waves, tsunamis, and hurricanes. The second part of this project investigates the dynamics of gasses and plasmas under physical kinetic boundary conditions, which is expected to provide insight into important physical phenomena such as the solar wind, galactic nebulae, and the Van Allen radiation belt. The third part of this project explores the physical interactions between relativistic kinetic theory and gravitational models bringing potential to increase knowledge in astrophysics, such as in systems of galaxies, supernova explosions, models of the early universe, and the study of hot gases and plasmas. This project will support the education and training of postdoctoral researchers, graduate students, and undergraduate students through research mentoring and seminars. It aims to further the goal of developing a diverse and globally competitive STEM workforce and to improve STEM education at the collegiate level.

This research will focus on improving the local-in-time well-posedness for large initial data and the global-in-time well-posedness near equilibrium for various fundamental non-linear partial differential equations. It involves developing new methods for analyzing several different physical models. One part of this work is to study fluid dynamics problems with free boundaries, such as the study of the Muskat bubble problem in 2D and 3D. Another part of this work examines problems related to the non-cutoff Boltzmann equation and the Landau equation from kinetic theory with the physical kinetic boundary conditions. The third part studies the relativistic Boltzmann equation and the Einstein-Boltzmann system. These developments are expected to benefit both mathematical and physical research in the future.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2405685","Lipschitz optimization with contemporary structure","DMS","APPLIED MATHEMATICS","09/01/2024","08/13/2024","Adrian Lewis","NY","Cornell University","Standard Grant","Stacey Levine","08/31/2027","$300,000.00","","adrian.lewis@cornell.edu","341 PINE TREE RD","ITHACA","NY","148502820","6072555014","MPS","126600","075Z, 079Z","$0.00","Modern Data Science, with its emphasis on ""Big Data"", presents a challenge for more traditional mathematical disciplines like Optimization. The mathematical techniques to be developed as part of this project aim to transform the design and analysis of algorithms across Optimization, bridging from current scholarship to vital computation in Data Science, robust control engineering and beyond. Graduate students will be central to this research, working in collaboration with the principal investigator on methodology and computation as well as preparing journal articles and conference presentations. This research will be incorporated into graduate coursework, made broadly accessible to the scientific community through targeted expository articles, involve collaboration across diverse fields, and be disseminated in international lectures to audiences across science and engineering.

This project involves a multi-pronged approach to the fresh challenges posed by Big Data in contemporary optimization, relying heavily on the underlying problems' rich inherent mathematical structure. First, relying on the semi-algebraic nature of all computer-representable objectives, the project will extend classical Lojasiewicz-type rescaling techniques to design and analyze the complexity of first-order and active-set optimization algorithms in hyperbolic and other non-Euclidean and infinite-dimensional settings. Such nonlinear spaces model diverse data, ranging from mass distributions separated by Wasserstein earth-mover distances, to phylogenetic trees in Computational Biology. Secondly, the principal invesigator will analyze condition measures of nonsmoothness and nonconvexity in Lipschitz optimization, and their impact on popular computational heuristics: such heuristics apparently converge nearly linearly and yet currently lack rigorous complexity guarantees. To this end, the project pursues a shift from point- to path-based analysis, and to distributional derivatives. Thirdly, informed by these condition measures, the project envisages reliable new algorithms, fast and intuitive enough to satisfy practitioners in Machine Learning, High-Dimensional Statistics, and Imaging Science, and also (at more moderate scale) in Systems Control and beyond. The project thus pursues a transformation of the modern continuous optimization toolkit, with potential impact across the computational sciences.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2406816","Analytical Challenges Near Dynamical Thresholds for Nonlinear Wave and Fluid Equations","DMS","APPLIED MATHEMATICS","09/01/2024","08/19/2024","Benjamin Harrop-Griffiths","DC","Georgetown University","Standard Grant","Dmitry Golovaty","08/31/2027","$186,811.00","","benjamin.harropgriffiths@georgetown.edu","MAIN CAMPUS","WASHINGTON","DC","200570001","2026250100","MPS","126600","","$0.00","A vast number of physical systems, from water flowing down a canal to light traveling through an optical fiber, involve the nonlinear interaction of waves. These interactions are typically described by scientists and engineers using partial differential equations. Frequently, a given equation will exhibit multiple different qualitative behaviors depending on the model?s parameters or data. This project seeks to understand solutions to these equations that live on the verge of two or more different dynamical regimes. Solutions near these ?dynamical thresholds? are key to understanding when a given equation is a faithful representation of some underlying physical system, and when it is not. The results of this investigation will not only yield new mathematical insights but also help to elucidate the possible uses and limitations of these models. In addition to these research goals, this project includes several educational and outreach activities, including training opportunities for both graduate and undergraduate students.


This project consists of three distinct problems. While the notion of what constitutes a dynamical threshold in each problem varies, what ties them together is a common set of mathematical tools with their foundations in real and harmonic analysis, spectral theory, and dynamical systems. The first problem considers solutions to integrable partial differential equations. Using recent developments in the analysis of these equations, the principal investigator (PI) will study dispersive estimates and soliton stability up to the threshold of ill-posedness. The second problem concerns certain toy models for wave turbulence. By incorporating tools from probability and combinatorics, the PI will seek to describe the effective dynamics up to the timescale at which the kinetic description breaks down. The final problem considers vortex filaments ? fluid configurations with vorticity concentrated along a curve. As the circulation of a vortex filament increases, the evolution transitions from being dominated by dissipation to being dominated by transport. Informed by previous work, the PI will make progress toward rigorously justifying these dynamics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2406942","Collaborative Research: Emerging Applications of Self-Similarity in Dynamical Networks","DMS","APPLIED MATHEMATICS","08/15/2024","08/15/2024","Matthew Mizuhara","NJ","The College of New Jersey","Standard Grant","Stacey Levine","07/31/2027","$128,950.00","","mizuharm@tcnj.edu","2000 PENNINGTON RD","EWING","NJ","086181104","6097713255","MPS","126600","","$0.00","Networks of various kinds and scales arise across biological, social, and physical systems. Moreover, self-similarity manifests in real-world networks in multiple ways, from the hierarchical self-similarity of the Internet, to the fractal-like structure of dendritic trees of neurons and protein interaction networks, and to the multiscale organization of social and epidemiological networks. Mathematical modeling helps to understand the principles underlying network dynamics, which can be used for effective prediction and control of real-world networks. This research studies the implications of self-similar structure of networks on their emergent dynamics. It aims to bridge analytical theories of fractals and differential equations on fractals with applications in network science. A combination of techniques from the analysis on fractals and dynamical systems will be used to develop new tools for the analysis, prediction, and control of self-similar network dynamics. Graduate and undergraduate students will be trained and contribute to these research activities.

The principal investigators will develop a set of model problems aimed at elucidating dynamics of self-similar networks. They will consider the Kuramoto model of coupled phase oscillators on graphs approximating the Sierpinski Gasket and other fractals and analyze them using a combination of analytical and numerical techniques. The goal of the first project is to develop a geometric approach to the construction of harmonic maps from post-critically finite fractals to a circle. The outcomes of this project will be used to construct stable steady states of coupled oscillator models on graphs approximating these fractals. The second project is focused on synchronization and bifurcations in self-similar networks. The third project studies epidemiological networks based on an SIR (Susceptible-Infected-Removed) model on graphs approximating fractals. Combined these projects are expected to deliver a new set of tools for studying interacting dynamical systems on self-similar sets.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2407058","RUI: Network Evolution with Unobserved Mechanisms","DMS","OFFICE OF MULTIDISCIPLINARY AC, APPLIED MATHEMATICS, Human Networks & Data Sci Res","08/15/2024","08/14/2024","Philip Chodrow","VT","Middlebury College","Standard Grant","Stacey Levine","07/31/2027","$287,522.00","","pchodrow@middlebury.edu","9 OLD CHAPEL RD","MIDDLEBURY","VT","057536000","8024435000","MPS","125300, 126600, 147Y00","9150, 9229","$0.00","Many social networks evolve through mechanisms that are only partially recorded in data. For example, the observed formation of a link between two new friends in a social network might depend on an unobserved third person who introduced them. In this project, the investigators will develop new mathematical models of social networks which evolve through unobserved events and use these models to analyze real-world data. The research team will focus on two broad phenomena to model. First, they will study how networks of multiway interactions become segregated by agent attributes (such as gender, race, social class, or opinion on a topic) over time. The team will especially focus on how agents with minority attributes can come to occupy positions of visibility or power in such networks. Second, the team will study how social hierarchies shape and are shaped by networks of cooperative endeavor. This work will take place in collaboration with practicing anthropologists and theoretical biologists. The results of both workstreams will highlight the strengths and limitations of simple theories of human social behavior and will also generate novel analysis algorithms for several types of network data. A diverse group of undergraduate students will be recruited via a summer work-study program to pursue these workstreams. These students will collaborate on interdisciplinary teams, learning best practices for collaborative research alongside technical skills.

For each of the systems under study the team will pursue three primary technical tasks. The first task will be to perform data analysis and use this analysis to formulate a stochastic latent-variable model of the system. The second task will be to analyze the long-run behavior of each modeled system, with an eye towards detecting phase transitions: qualitative shifts in macroscopic behavior as system parameters are smoothly varied. The team will determine parameter regimes in which models of growing hypergraphs exhibit self-reinforcing segregation or in which models of cooperation exhibit stable social hierarchies. These phase transitions will be determined using compartmental equations and associated analysis. The third task will be to develop efficient algorithms for inference: learning model parameters from observed data. The team will approach the inference problem through the classical lens of maximum-likelihood estimation. To perform optimization efficiently in the latent-variable setting, the team will develop and implement expectation-maximization algorithms for these models. The team will also develop online stochastic variants specialized for the case of very large data. In the case of hypergraph segregation models, the inference framework will lead to novel algorithms for model-based hypergraph clustering, while in the case of cooperative hierarchies inference will lead to novel dynamic embedding algorithms for time-stamped undirected graphs. The team will validate the proposed models through parameter recovery experiments on synthetic data. The team will then use these models to analyze real-world network data sets across several social domains.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2408264","Analysis of Nonlinear Partial Differential Equations including Boundary Value problems in Kinetic Theory, Free Boundary Fluid Dynamics, and the Einstein-Boltzmann system","DMS","APPLIED MATHEMATICS","08/15/2024","08/13/2024","Robert Strain","PA","University of Pennsylvania","Standard Grant","Hailiang Liu","07/31/2027","$300,000.00","","strain@math.upenn.edu","3451 WALNUT ST STE 440A","PHILADELPHIA","PA","191046205","2158987293","MPS","126600","","$0.00","This project aims to advance the mathematical analysis of non-linear partial differential equations used in a wide range of applications. The first part of this project involves the study of fluid dynamics problems with free boundaries, aimed at enhancing the understanding of water waves, tsunamis, and hurricanes. The second part of this project investigates the dynamics of gasses and plasmas under physical kinetic boundary conditions, which is expected to provide insight into important physical phenomena such as the solar wind, galactic nebulae, and the Van Allen radiation belt. The third part of this project explores the physical interactions between relativistic kinetic theory and gravitational models bringing potential to increase knowledge in astrophysics, such as in systems of galaxies, supernova explosions, models of the early universe, and the study of hot gases and plasmas. This project will support the education and training of postdoctoral researchers, graduate students, and undergraduate students through research mentoring and seminars. It aims to further the goal of developing a diverse and globally competitive STEM workforce and to improve STEM education at the collegiate level.

This research will focus on improving the local-in-time well-posedness for large initial data and the global-in-time well-posedness near equilibrium for various fundamental non-linear partial differential equations. It involves developing new methods for analyzing several different physical models. One part of this work is to study fluid dynamics problems with free boundaries, such as the study of the Muskat bubble problem in 2D and 3D. Another part of this work examines problems related to the non-cutoff Boltzmann equation and the Landau equation from kinetic theory with the physical kinetic boundary conditions. The third part studies the relativistic Boltzmann equation and the Einstein-Boltzmann system. These developments are expected to benefit both mathematical and physical research in the future.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2405685","Lipschitz optimization with contemporary structure","DMS","APPLIED MATHEMATICS","09/01/2024","08/13/2024","Adrian Lewis","NY","Cornell University","Standard Grant","Stacey Levine","08/31/2027","$300,000.00","","adrian.lewis@cornell.edu","341 PINE TREE RD","ITHACA","NY","148502820","6072555014","MPS","126600","075Z, 079Z","$0.00","Modern Data Science, with its emphasis on ""Big Data"", presents a challenge for more traditional mathematical disciplines like Optimization. The mathematical techniques to be developed as part of this project aim to transform the design and analysis of algorithms across Optimization, bridging from current scholarship to vital computation in Data Science, robust control engineering and beyond. Graduate students will be central to this research, working in collaboration with the principal investigator on methodology and computation as well as preparing journal articles and conference presentations. This research will be incorporated into graduate coursework, made broadly accessible to the scientific community through targeted expository articles, involve collaboration across diverse fields, and be disseminated in international lectures to audiences across science and engineering.

This project involves a multi-pronged approach to the fresh challenges posed by Big Data in contemporary optimization, relying heavily on the underlying problems' rich inherent mathematical structure. First, relying on the semi-algebraic nature of all computer-representable objectives, the project will extend classical Lojasiewicz-type rescaling techniques to design and analyze the complexity of first-order and active-set optimization algorithms in hyperbolic and other non-Euclidean and infinite-dimensional settings. Such nonlinear spaces model diverse data, ranging from mass distributions separated by Wasserstein earth-mover distances, to phylogenetic trees in Computational Biology. Secondly, the principal invesigator will analyze condition measures of nonsmoothness and nonconvexity in Lipschitz optimization, and their impact on popular computational heuristics: such heuristics apparently converge nearly linearly and yet currently lack rigorous complexity guarantees. To this end, the project pursues a shift from point- to path-based analysis, and to distributional derivatives. Thirdly, informed by these condition measures, the project envisages reliable new algorithms, fast and intuitive enough to satisfy practitioners in Machine Learning, High-Dimensional Statistics, and Imaging Science, and also (at more moderate scale) in Systems Control and beyond. The project thus pursues a transformation of the modern continuous optimization toolkit, with potential impact across the computational sciences.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2408635","A new class of high-order integral solvers for wave propagation problems in composite media","DMS","APPLIED MATHEMATICS","08/15/2024","08/07/2024","Catalin Turc","NJ","New Jersey Institute of Technology","Continuing Grant","Stacey Levine","07/31/2027","$72,000.00","","cat.c.turc@gmail.com","323 DR MARTIN LUTHER KING JR BLV","NEWARK","NJ","071021824","9735965275","MPS","126600","","$0.00","This project is concerned with the design and the analysis of computational methodologies aimed at solving applied problems in materials science and engineering involving various physical observables (elastic and electromagnetic fields, acoustic fields in the frequency and the time domain) within and around complex structures (photonic or electronic devices, singular geometries with corners, edges or cracks, manmade structures built from metals or modern composite materials). The approaches also address frameworks containing complex materials?including composite elastic media, dielectrics, perfect and lossy conductors, as well as clouds of scatterers that can be described by media with dispersion and frequency-dependent absorption. Motivating applications for the solvers to be developed in this project include the radar clutter produced by chaff, photonic crystals and metamaterials, and communications. These are of fundamental significance in a wide class of areas concerning photonics (meta-materials, nanophotonics, meta-surfaces), antenna design (communications, remote sensing), electromagnetic interference and compatibility, and geophysical exploration. High-quality software implementation of the algorithms to be developed as part of this project will be released to the applied scientific community. This project will have a significant educational component, as both graduate and undergraduate students will be trained in scientific computing and mathematical modeling, and thus they will acquire the skills required to have a successful career in academia or industry.

The computational methodologies underlying the proposed work are based on a class of density interpolations developed in recent years by the investigator and collaborators that is applicable to both Galerkin and Nystrom discretizations of all types of integral formulations. These methods combine the versatility of the Method of Fundamental Solutions with the robustness of integral formulations, are compatible with all kinds of meshes and quadratures, and can be seamlessly integrated with existing acceleration strategies such as Fast Multipole Methods. In practice, these types of solvers have demonstrated numerics that are fast and accurate for simulation of wave propagation problems in complex media, and thus they advance the state of the art in high-accuracy solution of partial differential equations. Owing to its ease of implementation and portability to solving a range of partial differential equations, the density interpolation method technology provides a vehicle to make integral equation solvers accessible to computational scientists from diverse backgrounds.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2407361","Reduced-Order Multiscale Models for Uncertainty Quantification, Data Assimilation and Control","DMS","APPLIED MATHEMATICS","08/15/2024","08/07/2024","Di Qi","IN","Purdue University","Standard Grant","Pedro Embid","07/31/2027","$203,648.00","","qidi@purdue.edu","2550 NORTHWESTERN AVE # 1100","WEST LAFAYETTE","IN","479061332","7654941055","MPS","126600","1303, 5294","$0.00","The mathematical study of turbulent flows requires models that can account for a large range of spatiotemporal scales, from small scale eddies to large scale coherent structures, the nonlinear interactions that are responsible for the transfer of energy across those scales, and statistical tools to account for the uncertainty and limited number of measurements available. Examples can be found in the study of atmospheric and oceanic flows, controlled plasma fusion, and other engineering applications. Due to their nonlinear coupling across a wide range of spatiotemporal scales, a rigorous analysis of these systems often becomes intractable and direct numerical simulations are likely to be expensive and inaccurate. The focus of this project is to develop a mathematical framework to derive tractable reduced-order models that effectively capture the dynamics of complex turbulent systems and apply them to complex systems of practical interest. This unified mathematical framework is based on the systematic integration of approaches from data assimilation, uncertainty quantification, and optimal control. The project will also provide training and research opportunities for undergraduate and graduate students.

This project will develop a general framework for the formulation of self-consistent reduced-order closure models for turbulent flows, with theoretical justifications and application to relevant fluid flow systems. The unified reduced-order model is achieved through a precise decomposition of the state of the system into low-order statistical moments that characterize the dominant, leading-order coherent structures, coupled with the stochastic fluctuations modes accounting for the higher-order non-Gaussian statistics quantifying the multiscale feedback. The reduced-order model will form the basis for new multiscale data assimilation strategies with partial and noisy data. In addition, the reduced-order model will be used to formulate new mean-field control models to drive the fluid system to a desired coherent state. The resulting methods will be applied to several concrete models for geophysical flows and plasma physics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2407006","Modeling and Analysis of Particle Laden Flow","DMS","APPLIED MATHEMATICS","09/01/2024","08/07/2024","Andrea Bertozzi","CA","University of California-Los Angeles","Continuing Grant","Pedro Embid","08/31/2029","$313,202.00","","bertozzi@math.ucla.edu","10889 WILSHIRE BLVD STE 700","LOS ANGELES","CA","900244200","3107940102","MPS","126600","","$0.00","This project involves modeling and analysis of particle laden flows using nonlinear partial differential equations (PDEs) for the flow thickness and volume fraction of particles in the flow. Such flows arise in many applications including the food industry, mining, and environmental cleanup. These flows are notoriously difficult to model because the dominant physics, especially for viscous flows, is due to many body interactions of the particles. There are no ""first principles"" continuum models for the physics and instead modelers rely on semi-empirical rules for particle settling and migration. Even at the elementary level of reduced order continuum theory, the mathematical equations are a system of conservation laws with fluxes that need to be estimated numerically. This project addresses fundamental mathematics problems related to these models. The project also develops new models for flows in complex geometries such as spiral separators used in the mining industry. This project is a five-year study that impacts our understanding of particle laden flow dynamics and analysis of PDEs for the novel fluid equations that model the physics of particle laden flows. In addition, this project provides research training for two doctoral students, five undergraduate researchers, and two postdoctoral scholars over a five-year period.

This project addresses several interrelated problems in particle laden flow models. (a) Flux functions in conservation law models for particle laden flow must be computed or estimated numerically. This raises the question of structural stability of multi-wave solutions of conservation laws under perturbation of the flux function. (b) Singular shocks have been shown to exist in conservation laws that model particle laden flow. Such solutions have largely, to date, been a curiosity in the mathematics literature. This project considers the actual physics that leads to singular shocks and studies how to continue those solutions after the singular shock formation in a way that is consistent with experimental observations. (c) This project considers models for bidisperse flows with direct comparison to experiments, building on earlier work for bidensity flows. (d) Spiral Separators are devices used in the mining industry in which slurries flow under gravity in a helical trough and species within the slurry naturally separate through turns of the spiral, coming out as stripes at the end. This project develops an asymptotic model for two species flows in spiral separators and studies how to optimally separate the species.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -18,20 +20,20 @@ "2406447","Inverse Boundary Value Problems","DMS","APPLIED MATHEMATICS","08/15/2024","08/07/2024","Gunther Uhlmann","WA","University of Washington","Standard Grant","Stacey Levine","07/31/2027","$300,000.00","","gunther@math.washington.edu","4333 BROOKLYN AVE NE","SEATTLE","WA","981951016","2065434043","MPS","126600","","$0.00","The ability to determine the internal properties of a medium by making measurements at the boundary of the medium provides important insight in a wide range of scientific applications. The question is whether one can one ""see"" what is inside the medium by making measurements on the outside. This project involves establishing a deeper mathematical understanding of the inverse imaging technique called electrical impedance tomography (EIT), which arises both in medical imaging and geophysics. EIT attempts to determine the electrical properties of an object by making voltage and current measurements from electrodes located at the boundary of the object. This project will also investigate the question of determining the inner structure of the Earth by measuring the travel times of earthquakes measured at different seismic stations located throughout the Earth. Graduate students will be trained and contribute to these projects.

This project will address the mathematical theory of several fundamental inverse problems arising in many areas of science and technology including medical imaging, geophysics, astrophysics and nondestructive testing, to name a few. Three topics of research will be addressed. The first one is Electrical Impedance Tomography (EIT), also called Calderon?s problem. The second topic is travel time tomography in anisotropic media. The third topic is inverse problems for non-linear hyperbolic equations. EIT is an inverse method used to determine the conductivity of a medium by making voltage and current measurements at the boundary. Specific projects will address mathematical challenges in developing and understanding the frameworks that address the case of partial data, anisotropic conductors, the recovery of discontinuities of a medium from boundary information, quasilinear model equations, and high frequencies for anisotropic media. An understanding of travel time tomography involves the determination of a Riemannian metric (anisotropic sound speed) in the interior of a domain from the lengths of geodesics joining points of the boundary (travel times) and from other kinematic information. This project will address the two dimensional scenario, the range characterization and boundary rigidity for simple manifolds, and a novel metric from the area of minimal surfaces bounded by closed curves on the boundary. The investigator will also develop a framework for using the interaction of waves to create new waves that will give information about the object being probed. Specific topics include the study of an inverse problem for the non-linear Klein Gordon equation and inverse problems arising in fluid dynamics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2406283","Aviles-Giga Conjecture, Differential Inclusions and Rigidity","DMS","APPLIED MATHEMATICS","08/15/2024","08/07/2024","Andrew Lorent","OH","University of Cincinnati Main Campus","Standard Grant","Dmitry Golovaty","07/31/2027","$149,999.00","","andrew.lorent@uc.edu","2600 CLIFTON AVE","CINCINNATI","OH","452202872","5135564358","MPS","126600","","$0.00","The project aims to advance understanding of some key problems in the field of Calculus of Variations, specifically the Aviles-Giga conjecture, and more broadly, how restrictions on gradients of functions imply rigidity, stability, and compactness properties. The Aviles-Giga conjecture is a central open problem in the Calculus of Variations, modeling phenomena such as thin film blistering and micromagnetics. The conjecture seeks to provide a mathematical justification for a scaling law observed in physics, leading to more accurate modeling of certain physical phenomena. Part of the conjecture involves sharp regularity estimates for a well-studied class of equations known as Eikonal equations, which arise in liquid crystal models and optics. These estimates are valuable for numerically solving such equations and are of broad mathematical interest. The Aviles-Giga theory is closely connected to the theory of scalar conservation laws, and its methods are being applied to understand a class of solutions of scalar conservation laws that arise in probability, specifically the large deviation conjecture. The project also aims to propagate its outcomes through seminars, lectures, graduate student recruitment, and the research produced.

The project consider problems in Calculus of Variations. The first problem is the Aviles-Giga conjecture, where the main open problem is showing that the energy concentrates, as it is not even known if the measure representing the limiting energy is singular. Achieving this goal would lead to a complete understanding of the regularizing properties of the Eikonal equation on the Besov scale. The second problem deals with quantitative rigidity for non-elliptic differential inclusions and builds on a previous result for rotation matrices and an optimal generalization to connected 1D elliptic curves in the space of two-by-two matrices. One of the purpose of this work is a more general regularity/rigidity theory for non-elliptic curves. The third project studies compensated compactness and conservation laws in higher dimensions. Reformulating regularity and uniqueness questions of PDEs as differential inclusions has led to the solution of a number of outstanding conjectures. This part of the research focuses on further developing methods initiated by the principal investigator and collaborators to study the differential inclusion problem related to regularity and uniqueness questions for conservation laws in higher dimensions. The final project on gamma-convergence for the Bellettini-Bertini-Mariani-Novaga functional considers a proposed gamma-limit related to certain conjectures in large deviation theory. The project focuses on a special case of this conjecture.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2408585","Analysis of Continuum PDE's in Collective Behavior and Related Models","DMS","APPLIED MATHEMATICS","08/15/2024","08/05/2024","Trevor Leslie","IL","Illinois Institute of Technology","Standard Grant","Hailiang Liu","07/31/2027","$150,000.00","","tleslie@iit.edu","10 W 35TH ST","CHICAGO","IL","606163717","3125673035","MPS","126600","","$0.00","This project concerns the fundamental mechanisms underpinning collective behavior of large groups of agents, such as flocks of birds, schools of fish, or swarms of bacteria. Mathematical models for these phenomena offer insights into how large-scale structures emerge from small-scale interactions in physical systems, with potential applications in technology, including in computer graphics. In order to efficiently study systems with an otherwise intractable number of agents, this project will focus on the ""effective"" large-scale dynamics rather than on individual trajectories. Taking this perspective brings the problems of interest into the realm of partial differential equations. The models that arise in these problems bear substantial resemblance to equations found in fluid dynamics and continuum mechanics, a connection that will be leveraged extensively in the research to be carried out. The mentorship, training, and professional development of students and junior researchers will also be a key goal of the project.

The proposed analysis will center on the effects of a nonlocal velocity alignment mechanism in isolation, as manifested in the class of hydrodynamic equations known as Euler Alignment systems. The PI will investigate the consequences of imposing different communication rules, especially as they relate to the large-time structure and regularity of the density profile. Emphasis will be placed on the as-of-yet poorly understood transition between qualitatively different regimes of interactions. In particular, the PI will leverage the additional structure available in settings with simple geometries to draw connections between models that incorporate strongly localized alignment and those that feature sticky particles. The PDEs governing alignment dynamics serve as a paradigm for more general nonlocal equations, and the proposed research has the potential to advance the understanding of classes of nonlocal models far beyond those explicitly studied in the project.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2407456","Inverse problems based on seismology and magnetohydrodynamics of solar system gas giants","DMS","APPLIED MATHEMATICS","09/01/2024","07/31/2024","Maarten de Hoop","TX","William Marsh Rice University","Standard Grant","Stacey Levine","08/31/2027","$310,000.00","","mdehoop@rice.edu","6100 MAIN ST","Houston","TX","770051827","7133484820","MPS","126600","","$0.00","Revealing the interiors, and constraining the equations of state (describing how materials behave under realistic pressure and temperature conditions), of gas giant planets in the solar system have been important objectives in planetary science, even more so since the detection of many gaseous exoplanets. These exoplanets are being examined to learn more about how the solar system came to be, and to compare the formation of our solar system to those planetary systems. Seismology has been playing a role in obtaining (instantaneous) models of gas giant planets, including their layering and equations of state, while planetary magnetic fields have been informing one further about their interior properties and thermal evolution. This project involves a novel mathematical framework to facilitate gaining new insights in the (new class of) inverse problems associated with seismology and magnetohydrodynamcs describing the generation of magnetic fields through dynamos. The project offers, via collaborations, a unique interdisciplinary educational experience for the students giving them a much broader appreciation of the importance of novel techniques and implications in space exploration.

The principal investigator will study inverse problems for revealing the interiors of gas giant planets, that is, Saturn and Jupiter, in the solar system, pertaining to seismology and magnetohydrodynamics. Both are mathematically fundamentally distinct from their treatments on Earth and raise intriguing challenges in their analyses. These inverse problems are defined through systems of linear(ized) partial differential equations describing acoustic-gravitational oscillations and nonlinear partial differential equations describing magnetohydrodynamics (in the Boussinesq approximation) as well as edge operators. The project is foundational, but its significance extends to the data that have and will become available from NASA's Cassini and Juno missions; the investigator collaborates with members of the Science Team of the second mission. The results will contribute to discerning limits and possibilities, including guarantees of reliability or lack thereof.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2407692","Self-supervised Probabilistic Graph Structure Learning for Task-agnostic Latent Representation","DMS","OFFICE OF MULTIDISCIPLINARY AC, APPLIED MATHEMATICS","09/01/2024","08/02/2024","Li Wang","TX","University of Texas at Arlington","Continuing Grant","Stacey Levine","08/31/2027","$229,461.00","Ren-Cang Li","li.wang@uta.edu","701 S NEDDERMAN DR","ARLINGTON","TX","760199800","8172722105","MPS","125300, 126600","075Z, 079Z","$0.00","Graphs provide simple and yet powerful mathematical structures to describe pairwise connections among different parties while providing a natural way to develop a deep understanding for real-world environments. There are many situations, however, where graph connections are not readily apparent or are completely hidden. For example, hidden within mountainous microarray data from breast cancer are tree-structure graphs that can delineate breast cancer progressions from one stage to another and thereby are extremely helpful for doctors to devise the best treatment plan for a particular breast cancer survivor. Because they are hidden, the underlying graphical characteristics are not obvious to see and must be learned with intelligent learning models. In this project, the investigators plan to develop and analyze novel graph structure learning models that can uncover latent representations hidden within big data applications. Students will be trained as part of this project, working on the development of mathematical models, numerical algorithms, and software packages for public distribution.

This project involves the development and analysis of advanced models and efficient algorithms for latent representation learning via self-supervised graph structure learning. Departing from existing methods, the proposed research tackles task-agnostic graph structure learning so as to not only broaden learning on various types of data, e.g., non-graph data or graph data with unreliable graphs, but also be generalizable, transferrable and robust to different learning tasks. Specifically, new self-supervised probabilistic graph structure learning models, including novel deep graph learning architecture extensions for single and multi-view data, will be formulated to increase the expressive power of the learners, and efficient algorithms to boost task-agnostic graph-based learning from shallow and deep perspectives will be developed to go with the new advanced mathematical models. The research results will appear as a combination of scientific publications and open-source and freely downloadable packages that can be used by researchers in diverse disciplines.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2407055","Stochastic Nash Evolution","DMS","OFFICE OF MULTIDISCIPLINARY AC, APPLIED MATHEMATICS","08/15/2024","08/02/2024","Govind Menon","RI","Brown University","Standard Grant","Dmitry Golovaty","07/31/2027","$300,000.00","","menon@dam.brown.edu","1 PROSPECT ST","PROVIDENCE","RI","029129100","4018632777","MPS","125300, 126600","9150","$0.00","This project develops a new framework for the Nash embedding theorems in order to align the foundations of mathematics with cutting edge scientific applications, especially in AI. In the 1950s, Nash amazed the mathematical world by unifying two distinct ways of thinking about space. In two papers, he established that an abstractly defined space with a notion of length (an intrinsic Riemannian manifold) can be realized as the solution of a system of nonlinear differential equations (an extrinsic embedded manifold). These theorems are strikingly original. For example, a counterintuitive conclusion is that it is possible to crumple the surface of the globe into an arbitrarily small region without any change in length. In a remarkable development in the past decade, these theorems are now known to lie at the foundation of outstanding scientific challenges, especially the description of turbulence in fluids and the description of big data with deep learning. This project tackles both theory and practice. On one hand, a rigorous mathematical framework is developed for the Nash embedding theorems using probability theory, shedding new light on the underlying concepts and techniques. On the other hand, algorithms and models are developed that align the theory with scientific applications. The project contributes to the training of personnel in STEM fields through the mentoring of Ph.D students.

The technical core of this project is the rigorous analysis of Riemannian Langevin equations (RLE). The RLE provides a unified model in geometric deep learning, random matrix theory, and the isometric embedding problem (and related nonlinear PDE). In each setting, the goal of this project is to rigorously construct Gibbs measures in tandem with the development of fast optimization and sampling algorithms. Regarding mathematical foundations, the primary focus is on new intrinsic constructions of Brownian motion on Riemannian manifolds and the construction of stochastic flows with critical regularity. This framework is then extended to turbulence and other h-principles in PDE, replacing Nash's iterative scheme with RLE in each case. Matrix models, especially the deep linear network (DLN), provide the bridge between geometry and algorithms. On one hand, the Riemannian geometry of DLN is used to guide the analysis of (nonlinear) deep learning. On the other hand, the use of stochastic gradient descent is used to develop numerical schemes for sampling Gibbs measures for nonlinear PDE.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2406896","Nonconvex optimization for deep graph learning: modeling and algorithms","DMS","OFFICE OF MULTIDISCIPLINARY AC, APPLIED MATHEMATICS","09/01/2024","08/02/2024","Yangyang Xu","NY","Rensselaer Polytechnic Institute","Standard Grant","Stacey Levine","08/31/2027","$249,999.00","","xuy21@rpi.edu","110 8TH ST","TROY","NY","121803590","5182766000","MPS","125300, 126600","075Z, 079Z","$0.00","Graph-structured data appear in many applications such as social networks, functional brain networks, and protein-protein interaction networks. Graph convolutional networks have demonstrated significant performance improvements over traditional methods for performing large scale graph tasks due to their learnable parameters that can capture more and task-adaptive information. Despite the success of graph convolutional networks, accurate and efficient algorithm development is still in its early stages. This proposal focuses on addressing the challenges for handling large-scale graph tasks using graph convolutional networks. New models will be built to produce task-desired solutions and to exploit feature information in challenging large-scale graph tasks. Novel numerical approaches will be designed to solve existing and new-built models in an efficient and reliable way. This project aims at achieving good practical performance on real graph tasks, provably fast convergence for the designed algorithms, and low overall complexity in computing numerical solutions. The project will involve graduate and undergraduate students, in particular underrepresented students in STEM, by involving them in research activities. The research findings will be integrated into curricula, thus impacting both undergraduate and graduate education.

Novel mathematical models and algorithms for deep graph learning will be designed and analyzed. First, variance-reduced neighbor sampling approaches and a new constrained optimization model aimed at enabling more efficient algorithms will be designed for deep graph representation learning. Asynchronous parallel versions of these new methods will also be developed to increase efficiency. Second, new deep graph representation learning -assisted models will be built for graph matching, by using sparsity-promoting regularizers or penalty terms that can lead to task-desired solutions. On solving the new models, accelerated low-order methods will be designed by using the proposed variance-reduced neighbor sampling and momentum acceleration techniques, under the framework of the augmented Lagrangian method or the alternating minimization. Third, new models with finite-sum structured nonconvex constraints will be built for graph clustering by using deep graph representation learning to exploit feature information. Variance-reduced stochastic methods will be designed to solve the models by exploiting the finite-sum structure. These investigations are expected to lead to novel models and efficient algorithms for large-scale graph tasks that currently cannot be completed in an accurate and/or efficient way.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2406767","New routes to broadband wave turbulence","DMS","APPLIED MATHEMATICS","09/01/2024","08/02/2024","Oliver Buhler","NY","New York University","Standard Grant","Pedro Embid","08/31/2027","$339,994.00","","obuhler@cims.nyu.edu","70 WASHINGTON SQ S","NEW YORK","NY","100121019","2129982121","MPS","126600","","$0.00","Small-scale wave motions in the atmosphere and oceans are ubiquitous and well-known to contribute significantly to the long-term global-scale evolution of these system, yet their direct numerical simulation remains elusive with present-day computational capacities. This leads to the necessity of understanding their dynamics from a fundamental theoretical perspective, which ultimately allows their impact on the global-scale dynamics to be modeled in a systematic and rational fashion. Early theoretical efforts were based on monochromatic wave models, i.e., they were based on studying a single wave interacting with its environment. More recently the theoretical focus has expanded to the more complicated and more realistic model of allowing a broad spectrum of waves to be present simultaneously. This is much closer to real atmosphere/ocean waves, and it also encompasses the study of the mutual interactions of many different wave components, which produces a peculiar dynamical evolution scenario known as wave turbulence. The present project focuses on internal gravity waves in the ocean, which owe their restoring mechanism to a combination of gravitational density stratification and the background rotation of planet Earth. This project will also provide opportunities for the integration of students into the research.

The project seeks to break new ground with a multi-pronged approach that combines theory and numerical modeling in three problem areas. First, it builds on previous theoretical advances in the study of how broadband wave spectra can be created from monochromatic sources via interactions with mean currents. Novel questions to be addressed include a study of the convergence or divergence of Lagrangian and Eulerian wave spectra, which is crucial to compare to observations. Second, recent results indicate that dual cascades based on twin conservation laws behave quite differently in hydrodynamic turbulence and in wave turbulence. This will be explored based on a new stochastic model that is surprisingly successful in predicting the observed wave turbulence spectral dynamics. Third, abstract theory suggests that strongly directional wave turbulence could undergo a kind of phase transition whereby the nonlinear transfer of wave energy across the scales reverses direction, so wave energy might flow upscale rather than downscale. This will be investigated in simple models that also touch on other fundamental questions related to the importance of conservation laws that are not sign-definite.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2407456","Inverse problems based on seismology and magnetohydrodynamics of solar system gas giants","DMS","APPLIED MATHEMATICS","09/01/2024","07/31/2024","Maarten de Hoop","TX","William Marsh Rice University","Standard Grant","Stacey Levine","08/31/2027","$310,000.00","","mdehoop@rice.edu","6100 MAIN ST","Houston","TX","770051827","7133484820","MPS","126600","","$0.00","Revealing the interiors, and constraining the equations of state (describing how materials behave under realistic pressure and temperature conditions), of gas giant planets in the solar system have been important objectives in planetary science, even more so since the detection of many gaseous exoplanets. These exoplanets are being examined to learn more about how the solar system came to be, and to compare the formation of our solar system to those planetary systems. Seismology has been playing a role in obtaining (instantaneous) models of gas giant planets, including their layering and equations of state, while planetary magnetic fields have been informing one further about their interior properties and thermal evolution. This project involves a novel mathematical framework to facilitate gaining new insights in the (new class of) inverse problems associated with seismology and magnetohydrodynamcs describing the generation of magnetic fields through dynamos. The project offers, via collaborations, a unique interdisciplinary educational experience for the students giving them a much broader appreciation of the importance of novel techniques and implications in space exploration.

The principal investigator will study inverse problems for revealing the interiors of gas giant planets, that is, Saturn and Jupiter, in the solar system, pertaining to seismology and magnetohydrodynamics. Both are mathematically fundamentally distinct from their treatments on Earth and raise intriguing challenges in their analyses. These inverse problems are defined through systems of linear(ized) partial differential equations describing acoustic-gravitational oscillations and nonlinear partial differential equations describing magnetohydrodynamics (in the Boussinesq approximation) as well as edge operators. The project is foundational, but its significance extends to the data that have and will become available from NASA's Cassini and Juno missions; the investigator collaborates with members of the Science Team of the second mission. The results will contribute to discerning limits and possibilities, including guarantees of reliability or lack thereof.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2409926","Design and computation of origami-inspired structures and metamaterials","DMS","APPLIED MATHEMATICS","08/01/2024","08/01/2024","Frederic Marazzato","AZ","University of Arizona","Continuing Grant","Ludmil T. Zikatanov","07/31/2027","$49,680.00","","marazzato@arizona.edu","845 N PARK AVE RM 538","TUCSON","AZ","85721","5206266000","MPS","126600","9263","$0.00","Origami is the art of folding paper into intricate forms. Structures composed of origami patterns have been used for decades in the space industry as they are very compact when folded and can unfold into intricate shapes. More recently, Origami structure have been used to produce inexpensive mechanical metamaterials. Mechanical metamaterials are novel materials that present mechanical properties that are not common to usual materials. However, the design possibilities offered by origami structures remain presently mostly unexplored. This project will develop models and numerical methods to compute new origami patterns and study their deformation. The tools developed in this project will enable engineers to design new origami patterns with new properties and therefore create new metamaterials and foldable structures. Possible applications include designing structures that unfold into a target shape or designing micro-structures to obtain a desired macroscopic property.

This project will contribute to the study of the direct and inverse problems of designing origami structures. In the direct problem, one chooses a given periodic folding pattern and derives Partial Differential Equations (PDEs) describing the kinematics and energy of the limit surface. One then wants to study and approximate the solutions of PDE constrained optimization problems where the PDEs are nonlinear and can change type (between elliptic and hyperbolic) and degenerate. This project will use careful regularizations and nonconforming finite element discretizations in order to approximate the solutions of these difficult problems. The inverse problem consists in determining a crease pattern that will allow to fold from a flat state into a given target surface. Determining if a given pattern is flat foldable is known to be NP-hard. This project proposes to represent possible fold lines by damage in an elastic sheet and then to adapt the method of Ambrosio and Tortorelli to approximate minimizers of the Mumford--Shah functional. This will produce folding patterns on an initially flat surface which will be able to fold into the target surface. As paper deforms isometrically, this project intends to explore the approximation of nonzero Gauss curvature target surfaces to determine if notable properties emerge.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2407669","Collaborative Research: Stochastic Functional Systems: Analysis, Algorithms and Applications","DMS","OFFICE OF MULTIDISCIPLINARY AC, APPLIED MATHEMATICS","08/01/2024","08/01/2024","Nhu Nguyen","RI","University of Rhode Island","Standard Grant","Pedro Embid","07/31/2027","$198,173.00","","nhu.nguyen@uri.edu","75 LOWER COLLEGE RD RM 103","KINGSTON","RI","028811974","4018742635","MPS","125300, 126600","075Z, 079Z, 9150","$0.00","The time evolution of many physical, biological, and engineering systems is described by functional differential equations, where the future state of the system is not only determined by its present state, but also by the state of the system at some prior time(s). Examples can be found in the study of epidemic and ecological models, multi-agent models in financial systems, neural network models, and other areas in statistics, data science, and engineering. Among the various modeling approaches in existence, stochastic functional differential equations (SFDE) and McKean-Vlasov stochastic functional differential equations (MVSFDE) play a crucial role in modeling complex systems across science and engineering. Despite extensive research, many questions about these systems remain unresolved due to their challenging past-dependent nature. At the same time, a growing interest in functional stochastic approximation algorithms (FSAA) has emerged from new problems in optimization, data science, and machine learning. This project aims to systematically investigate these systems to establish their critical properties, broaden current applications, and discover new applications in science, machine learning, and engineering. In addition, this project will provide research opportunities for graduate students, engage high school students through math tournaments, and work towards creating a network of academia, students, and industry representatives to enhance career opportunities for students and increase public awareness of the role of mathematics in real-world applications.

This project aims to (i) explore long-term properties, such as ergodicity and stability, of SFDE; (ii) formulate a new approach for MVSFDE to systematically examine their fundamental properties and long-term behaviors; and (iii) propose a framework for FSAA dealing with discontinuous operators, establish convergence conditions and rates, and provide implementation methods. The project will apply these theories to address specific problems in ecology, infectious diseases, control engineering, networked systems, neutral network models, game theory, and cell biology, as well as emerging problems in statistics, data science, and engineering. To achieve these goals, the research will integrate Dupire's functional Itô's formula, inventive concepts of generalized coupling, and will bridge stochastic calculus and non-smooth analysis in infinite-dimensional spaces, in addition to employing other advanced techniques.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2420029","Hypoelliptic and Non-Markovian stochastic dynamical systems in machine learning and mathematical finance: from theory to application","DMS","APPLIED MATHEMATICS","02/01/2024","02/06/2024","Qi Feng","FL","Florida State University","Standard Grant","Pedro Embid","05/31/2026","$152,899.00","","qfeng2@fsu.edu","874 TRADITIONS WAY","TALLAHASSEE","FL","323060001","8506445260","MPS","126600","9251","$0.00","This project investigates stochastic analysis and numerical algorithms for stochastic dynamical systems, together with their applications in machine learning and finance. The first part focuses on the foundations of machine learning/data science, which guarantees the theoretical convergence of numerical algorithms (e.g., stochastic gradient descent, Markov Chain Monte Carlo) in non-convex optimization and multi-modal distribution sampling. This project will develop algorithms to solve such problems in big data and engineering, which include uncertainty quantification in AI safety problems, control robotics motions, and image processing. The second part focuses on the stochastic models in mathematical finance and algorithm designs in option/asset pricing. The applications in this part target efficient algorithms for path-dependent option pricing with rough volatilities, which are expected to significantly impact some computation-oriented financial instruments, such as model-based algorithm trading involving rough volatility and high-frequency data. This project will provide support and research opportunities for graduate and undergraduate students.

The stochastic systems in this project possess degenerate, mean-field, or non-Markovian properties. In the first part, the PI will study the ""hypocoercivity"" (i.e., convergence to equilibrium) for highly degenerate and mean-field stochastic dynamical systems and their applications to algorithms design in machine learning. One of the proposed topics will focus on the (non)-asymptotic analysis of the general degenerate/mean-field system and its exponential convergence rate to the equilibrium (e.g., Vlasov-Fokker-Planck equations; Langevin dynamics on higher order nilpotent Lie groups). As applications of the convergence of such dynamics, the PI will design algorithms focusing on non-convex optimizations and distribution samplings in machine learning. In the second part, the PI will study non-Markovian stochastic dynamical systems capturing path-dependent and mean-field features of the financial market. The topics include path-dependent PDEs, stochastic Volterra integral equations, conditional mean-field SDEs, and the Volterra signatures. The PI focuses on addressing the fundamental issues, including the density for the rough volatility model and conditional mean-field SDEs and the structure of Volterra signatures. Furthermore, the PI focuses on designing efficient numerical algorithms using the Volterra signature and deep neural networks. These algorithms target solving path-dependent PDEs, path-dependent option pricing, and optimal stopping/switching problems.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2406620","From Quantum Many-body Dynamics to Fluid Equations and Back","DMS","APPLIED MATHEMATICS","08/15/2024","08/02/2024","Xuwen Chen","NY","University of Rochester","Continuing Grant","Dmitry Golovaty","07/31/2027","$159,640.00","","xuwenmath@gmail.com","910 GENESEE ST","ROCHESTER","NY","146113847","5852754031","MPS","126600","","$0.00","The analysis, simulation, & applications of the nonlinear fluid equations like the Euler equations or the Navier-Stokes equations, is an important (if not a vital) part of many areas of Science, Technology, Engineering, and Mathematics (STEM). The research in this project concerns a variety of projects on the rigorous derivations of these macroscopic continuum equations from basic microscopic quantum particle models and elucidates how the macroscopic fluid-defining quantities like pressure or viscosity emerge from the averaging of microscopic quantities. Examples of the boson particles we study includes the nitrogen and oxygen molecules (99.03% volume of air) and 99.95% of the water molecules. The number of particles in these many-body systems is on the order of magnitude of the Avogadro constant, which make the microscopic simulation of such systems impossible. The mathematical justification of these macroscopic continuum limits for the many-body systems they are supposed to describe, is therefore an issue of fundamental scientific importance. The principal investigator is committed to introducing undergraduate and graduate students to experiments and cutting-edge mathematics, advising PhD students and mentoring postdoctoral researchers.

The particular scope of this research project is to investigate several problems concerning the fine properties of solutions to the time-dependent many-body Schrödinger equation when the particle number tends to infinity and the Planck constant tends to zero. This research project encompasses three broad directions. The first direction concerns the proof of the classical incompressible Euler equations as a direct limit of quantum many-body dynamics and find the microscopic quantity corresponding to the macroscopic Mach number. The second direction is to rigorously extract the hierarchy structure for the compressible Euler equations induced by quantum many-body dynamics and identify the microscopic quantity which becomes the macroscopic Knudsen number. The third direction turns to the study of the optimal well/ill-posedness separation and the fine nonlinear structure of solutions regarding the important mesoscopic Boltzmann equations via new dispersive methods. The PI and collaborators use techniques from harmonic analysis, probability, and spectral theory to analyze these problems.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2406293","Topics in Mathematical Biology and Fluids","DMS","OFFICE OF MULTIDISCIPLINARY AC, APPLIED MATHEMATICS","08/01/2024","07/31/2024","Siming He","SC","University of South Carolina at Columbia","Continuing Grant","Dmitry Golovaty","07/31/2027","$122,002.00","","siming@mailbox.sc.edu","1600 HAMPTON ST","COLUMBIA","SC","292083403","8037777093","MPS","125300, 126600","9150","$0.00","Transport and diffusion phenomena are ubiquitous in nature. For example, various important biochemical reactions take place in moving fluid flows. The reactant densities are transported by the flow and diffuse according to Fick's law. The principal investigator (PI) plans to develop a novel mathematical toolkit to describe the delicate interplay between transportation and diffusion in various physical and biological contexts. For instance, in specific scenarios, the ambient fluid flow can create small-scale structures in the densities involved and enhance their diffusion. A deeper understanding of this enhanced diffusion phenomenon has implications across various disciplines, ranging from stabilizing the chemotaxis process to improving communication efficiency in collective motions. Through detailed mathematical analysis, the PI plans to identify situations where this enhanced diffusion phenomenon plays a major role and to capture the interesting dynamics of the associated systems. The PI also plans to recruit talented undergraduate and graduate students to participate in this research project. Through this academic training, the PI hopes to equip the students with sufficient knowledge and skills to address future challenges that arise in science and technology.

This project aims to develop novel mathematical tools to analyze the long-time behaviors of coupled biology-fluid systems and transport-type equations arising in biological phenomena. The project addresses three main topics. In the first project, the PI plans to explore the delicate interaction between biological phenomena and their ambient fluid flows. Fluid transport phenomena can alter the overall qualitative features of biological processes. For example, the introduction of strong fluid flows can mitigate certain chemotaxis-induced concentration effects. The PI plans to develop mathematical tools to describe delicate interactions within coupled biology-fluid systems. In the second project, biological experiments guide the mathematical analysis. In the ocean, marine animals such as abalone release eggs and sperm in the fluid stream. Eggs emit chemical attractants while sperm aggregate towards them via random walk and chemotaxis. Once the gametes meet, the fertilization happens. Given that these processes occur in fluid flows effectively sheared on the length scales involved, it is biologically intriguing to study the relationship between fertilization rate and shear rate. The PI plans to develop faithful mathematical models and provide a convincing explanation for the experimental data from marine scientists. The third project focuses on hydrodynamic stability and small-scale creation in fluid mechanics. The PI plans to explore the stabilization mechanisms of shear flows in Navier-Stokes systems and investigate non-local models related to the Euler equation. A deeper understanding of these systems might be helpful in understanding the coupled biology-fluid systems.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2425995","Conference: The SIAM Quantum Intersections Convening","DMS","FET-Fndtns of Emerging Tech, OFFICE OF MULTIDISCIPLINARY AC, INFRASTRUCTURE PROGRAM, APPLIED MATHEMATICS, TOPOLOGY, FOUNDATIONS, STATISTICS, QIS - Quantum Information Scie, MATHEMATICAL BIOLOGY","08/01/2024","07/31/2024","Suzanne Weekes","PA","Society For Industrial and Applied Math (SIAM)","Standard Grant","Tomek Bartoszynski","07/31/2025","$349,996.00","","weekes@siam.org","3600 MARKET ST FL 6","PHILADELPHIA","PA","191042669","2153829800","MPS","089Y00, 125300, 126000, 126600, 126700, 126800, 126900, 728100, 733400","7203, 7556","$0.00","Society for Industrial and Applied Mathematics (SIAM) will host the SIAM Quantum Intersections Convening - Integrating Mathematical Scientists into Quantum Research to bring quantum-curious mathematical scientists together with leading experts in quantum science for a three-day interactive workshop. Recognizing the critical role of mathematical scientists, this convening aims to promote multidisciplinary collaborations that bridge the gap between mathematics and quantum sciences and aims to foster and increase the involvement and visibility of mathematicians and statisticians in quantum science research and education. The convening will be organized by a steering committee and will be supported by professional facilitators. Participants will learn from and connect with physicists, computer scientists, engineers and mathematical scientists who are experts in quantum science. This in-person gathering will be held in fall 2024 in the Washington DC area. A primary deliverable from the convening will be a report summarizing the activities and recommendations generated during the event. Key presentations will be recorded and will be available on a SIAM webpage.

Society for Industrial and Applied Mathematics (SIAM) will host this convening with the goals of (i) making more mathematical scientists aware of the demand for their expertise in quantum research and articulating areas and problems where they can contribute, (ii) increasing the participation of researchers in mathematical sciences in the quantum information science revolution to accelerate its research and development, (iii) providing a seeding ground for partnerships and collaborations of mathematical scientists with physicists, computer scientists, and engineers from industry and academia, and (iv) recommending activities to develop a quantum science and technology workforce pipeline in the mathematical and computational sciences. A few topics in quantum science where mathematics can help research and discovery include quantum computing, quantum algorithms, quantum optimization, quantum error corrections, quantum information theory, quantum cryptography, quantum sensing and metrology, and quantum networks.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2407358","Advancing Stability through Rigorous Computations","DMS","APPLIED MATHEMATICS","08/01/2024","07/31/2024","Jared Bronski","IL","University of Illinois at Urbana-Champaign","Continuing Grant","Dmitry Golovaty","07/31/2027","$282,599.00","Vera Mikyoung Hur","bronski@illinois.edu","506 S WRIGHT ST","URBANA","IL","618013620","2173332187","MPS","126600","","$0.00","Computers and computational methods are an increasingly important part of the scientific endeavor, and they are changing the ways in which science progresses. One new and important such methodology is that of validated numerics. Traditional numerical methods produce approximate solutions to the equation of interest. While these methods usually produce very good approximations to the exact solutions, they typically do not have explicit bounds on the error. In validated numerics the goal is to produce an approximate solution along with an explicit guarantee that the error is no larger than some prescribed tolerance. In practice realizing such a validated numerical method requires both new mathematical analysis and new computational techniques. On the computational side, for instance, rather than doing the standard floating point arithmetic one must instead do interval arithmetic, where the result of a calculation is not a single number but an interval in which the result is guaranteed to lie. While these validated numerical calculations are much more difficult to carry out than standard numerics, the advantage is that one has a mathematical proof of the correctness of the solution. This means that there are many questions about the behavior of solutions to equations to which one can give a mathematically rigorous numerical proof. The investigators study some equations that govern nonlinear wave phenomenon, such as the propagation of a wave in the ocean or light in an optical fiber. Often one can find an exact special solution to these equations, such as a wave that propagates without changing its shape. One would like to know if this solution is stable: if solutions that begin close to this known solution remain close. Stability is an important question from the point of view of applications, as it determines whether these solutions are likely to be observed in practice. The investigators study stability via validated numerics. An important part of this proposal is training graduate students in these increasingly important techniques.

The investigators address the stability of periodic traveling waves in Hamiltonian PDEs. One project establishes that the essential spectrum of the associated linearized operator to solutions of the generalized KdV and nonlinear Schrödinger equations is purely imaginary. This represents the first time that the essential spectrum has been calculated rigorously for such operators arising from non-integrable equations away from the small amplitude limit. This approach will extend to encompass other equations, including but not limited to regularized long wave type, the Benjamin-Ono and Camassa-Holm type, and two-dimensional equations. Furthermore, we aim to advance from spectral to linear stability, revealing the long-term dynamics of the solutions of the associated linearized equation.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2407197","Stochastic moving boundary problems in fluid-structure interaction","DMS","APPLIED MATHEMATICS","08/01/2024","07/31/2024","Krutika Tawri","CA","University of California-Berkeley","Continuing Grant","Pedro Embid","07/31/2027","$48,614.00","","ktawri@berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","126600","","$0.00","Fluid-Structure interaction (FSI) refers to physical systems whose behavior is dictated by the interaction of an elastic body and a fluid mass. The study of FSI is relevant to various applications, ranging from aerodynamics to biomechanics. To address the inherent numerical and physical uncertainties in these applications, it is common to introduce stochastic influences into mathematical models. This project takes an initial step in investigating the effects of stochastic forces on FSI models arising in biofluidic applications that describe the interactions between a viscous fluid, such as human blood, and an elastic structure, such as a human artery. Depending on the specific application, such as the location, roughness, and size of the vessel, various mathematical models will be explored. The proposed program opens a new class of problems in mathematics involving the study of stochastic partial differential equations (PDEs) posed on randomly moving domains, particularly when the displacement of the domain boundary is not known a priori. The aim of this project is to prove that the proposed stochastic FSI problems are well-posed and to study the properties of the solutions. Education and mentoring are important components of the project, with students involved in research activities. The writing of an expository book will also be undertaken.

The goal of this project is to provide existence results for a class of nonlinearly coupled stochastic FSI problems that includes a range of possibilities, such as compressible and incompressible fluid flows within thin or thick, linear or nonlinear elastic structures. Additionally, distinct coupling conditions, including the slip and no-slip kinematic coupling condition at the random and time-dependent fluid-structure interface, will be examined. Multiplicative white-in-time noise, applied both to the fluid as a volumetric body force and to the structure as an external forcing on the deformable fluid boundary, will be considered. The existence proof is based on semi-discretizing the multi-physics problem in time, decoupling the approximate problem using a penalty method, and employing an operator splitting strategy to split the fluid from the structure sub-problem(s), with the aid of a novel cut-off function approach coupled with a stopping time argument. The results of this research will shed light not only on the analytical properties of the solutions but also on the stability of the partitioned numerical schemes for stochastic FSI problems, ultimately providing insights into the robustness of these models against external noise. This study integrates tools from probability, differential geometry, and fluid dynamics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2407074","Price Impact and Optimal Transport","DMS","APPLIED MATHEMATICS","08/01/2024","07/31/2024","Marcel Nutz","NY","Columbia University","Standard Grant","Pedro Embid","07/31/2027","$250,000.00","","mnutz@columbia.edu","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","126600","075Z, 079Z","$0.00","This project studies (a) regularized optimal transport and (b) price impact in financial markets. Fueled by computational advances, optimal transport has become ubiquitous in applications from machine learning to image processing and economics. In such applications, optimal transport is often regularized with an entropic or quadratic penalty. Entropic regularization is the most frequent choice as it greatly facilitates computation and enhances smoothness. On the other hand, quadratic regularization is chosen when sparse solutions are desired. Studied mostly in the machine learning literature, its mathematical foundations are much less developed. The project will provide those foundations and theoretical guarantees for sparsity. Price impact in financial markets refers to the fact that prices are displaced during the execution of institutional-size orders; for instance, large buy orders push prices up. However, prices revert back over time. This resilience is vital for optimizing transaction costs in practice, but not modeled in many academic studies. The project features a range of broader impact activities, including advising and mentoring a diverse group of postdocs, graduate and undergraduate students, organizing interdisciplinary scientific meetings and summer schools, and serving on editorial boards and professional societies.

The first part of this project investigates entropically regularized optimal transport, where couplings are penalized by KL-divergence. Specifically, it studies the convergence of the optimal coupling as the regularization parameter tends to zero. The long-standing conjecture of entropic selection predicts that the optimal coupling converges to a certain solution of the unregularized optimal transport problem; that is, the limit selects a particular solution out of the possibly large set of optimal transports. The project aims to prove this in the most important setting, namely for Monge's distance cost. The second part of the project investigates quadratically regularized optimal transport, where couplings are penalized by the squared norm. It aims to analytically describe the empirically observed phenomenon of sparse support as well as the convergence for vanishing regularization, in both discrete and continuous settings. While quadratic regularization was mostly used in computational works so far, the project provides a robust mathematical toolbox for its study. The third part of the project investigates financial markets with transient price impact. The project studies predatory trading and liquidity provision, and in particular the regulatory issue of pre-hedging, in the presence of price impact and resilience. On the methodological side, it also establishes how to correctly formalize the Obizhaeva--Wang model (and related models) for non-cooperative games with price impact. Separately, the project studies the optimal execution of order flows for central risk books and market makers.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2406620","From Quantum Many-body Dynamics to Fluid Equations and Back","DMS","APPLIED MATHEMATICS","08/15/2024","08/02/2024","Xuwen Chen","NY","University of Rochester","Continuing Grant","Dmitry Golovaty","07/31/2027","$159,640.00","","xuwenmath@gmail.com","910 GENESEE ST","ROCHESTER","NY","146113847","5852754031","MPS","126600","","$0.00","The analysis, simulation, & applications of the nonlinear fluid equations like the Euler equations or the Navier-Stokes equations, is an important (if not a vital) part of many areas of Science, Technology, Engineering, and Mathematics (STEM). The research in this project concerns a variety of projects on the rigorous derivations of these macroscopic continuum equations from basic microscopic quantum particle models and elucidates how the macroscopic fluid-defining quantities like pressure or viscosity emerge from the averaging of microscopic quantities. Examples of the boson particles we study includes the nitrogen and oxygen molecules (99.03% volume of air) and 99.95% of the water molecules. The number of particles in these many-body systems is on the order of magnitude of the Avogadro constant, which make the microscopic simulation of such systems impossible. The mathematical justification of these macroscopic continuum limits for the many-body systems they are supposed to describe, is therefore an issue of fundamental scientific importance. The principal investigator is committed to introducing undergraduate and graduate students to experiments and cutting-edge mathematics, advising PhD students and mentoring postdoctoral researchers.

The particular scope of this research project is to investigate several problems concerning the fine properties of solutions to the time-dependent many-body Schrödinger equation when the particle number tends to infinity and the Planck constant tends to zero. This research project encompasses three broad directions. The first direction concerns the proof of the classical incompressible Euler equations as a direct limit of quantum many-body dynamics and find the microscopic quantity corresponding to the macroscopic Mach number. The second direction is to rigorously extract the hierarchy structure for the compressible Euler equations induced by quantum many-body dynamics and identify the microscopic quantity which becomes the macroscopic Knudsen number. The third direction turns to the study of the optimal well/ill-posedness separation and the fine nonlinear structure of solutions regarding the important mesoscopic Boltzmann equations via new dispersive methods. The PI and collaborators use techniques from harmonic analysis, probability, and spectral theory to analyze these problems.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2406293","Topics in Mathematical Biology and Fluids","DMS","OFFICE OF MULTIDISCIPLINARY AC, APPLIED MATHEMATICS","08/01/2024","07/31/2024","Siming He","SC","University of South Carolina at Columbia","Continuing Grant","Dmitry Golovaty","07/31/2027","$122,002.00","","siming@mailbox.sc.edu","1600 HAMPTON ST","COLUMBIA","SC","292083403","8037777093","MPS","125300, 126600","9150","$0.00","Transport and diffusion phenomena are ubiquitous in nature. For example, various important biochemical reactions take place in moving fluid flows. The reactant densities are transported by the flow and diffuse according to Fick's law. The principal investigator (PI) plans to develop a novel mathematical toolkit to describe the delicate interplay between transportation and diffusion in various physical and biological contexts. For instance, in specific scenarios, the ambient fluid flow can create small-scale structures in the densities involved and enhance their diffusion. A deeper understanding of this enhanced diffusion phenomenon has implications across various disciplines, ranging from stabilizing the chemotaxis process to improving communication efficiency in collective motions. Through detailed mathematical analysis, the PI plans to identify situations where this enhanced diffusion phenomenon plays a major role and to capture the interesting dynamics of the associated systems. The PI also plans to recruit talented undergraduate and graduate students to participate in this research project. Through this academic training, the PI hopes to equip the students with sufficient knowledge and skills to address future challenges that arise in science and technology.

This project aims to develop novel mathematical tools to analyze the long-time behaviors of coupled biology-fluid systems and transport-type equations arising in biological phenomena. The project addresses three main topics. In the first project, the PI plans to explore the delicate interaction between biological phenomena and their ambient fluid flows. Fluid transport phenomena can alter the overall qualitative features of biological processes. For example, the introduction of strong fluid flows can mitigate certain chemotaxis-induced concentration effects. The PI plans to develop mathematical tools to describe delicate interactions within coupled biology-fluid systems. In the second project, biological experiments guide the mathematical analysis. In the ocean, marine animals such as abalone release eggs and sperm in the fluid stream. Eggs emit chemical attractants while sperm aggregate towards them via random walk and chemotaxis. Once the gametes meet, the fertilization happens. Given that these processes occur in fluid flows effectively sheared on the length scales involved, it is biologically intriguing to study the relationship between fertilization rate and shear rate. The PI plans to develop faithful mathematical models and provide a convincing explanation for the experimental data from marine scientists. The third project focuses on hydrodynamic stability and small-scale creation in fluid mechanics. The PI plans to explore the stabilization mechanisms of shear flows in Navier-Stokes systems and investigate non-local models related to the Euler equation. A deeper understanding of these systems might be helpful in understanding the coupled biology-fluid systems.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2425995","Conference: The SIAM Quantum Intersections Convening","DMS","FET-Fndtns of Emerging Tech, OFFICE OF MULTIDISCIPLINARY AC, INFRASTRUCTURE PROGRAM, APPLIED MATHEMATICS, TOPOLOGY, FOUNDATIONS, STATISTICS, QIS - Quantum Information Scie, MATHEMATICAL BIOLOGY","08/01/2024","07/31/2024","Suzanne Weekes","PA","Society For Industrial and Applied Math (SIAM)","Standard Grant","Tomek Bartoszynski","07/31/2025","$349,996.00","","weekes@siam.org","3600 MARKET ST FL 6","PHILADELPHIA","PA","191042669","2153829800","MPS","089Y00, 125300, 126000, 126600, 126700, 126800, 126900, 728100, 733400","7203, 7556","$0.00","Society for Industrial and Applied Mathematics (SIAM) will host the SIAM Quantum Intersections Convening - Integrating Mathematical Scientists into Quantum Research to bring quantum-curious mathematical scientists together with leading experts in quantum science for a three-day interactive workshop. Recognizing the critical role of mathematical scientists, this convening aims to promote multidisciplinary collaborations that bridge the gap between mathematics and quantum sciences and aims to foster and increase the involvement and visibility of mathematicians and statisticians in quantum science research and education. The convening will be organized by a steering committee and will be supported by professional facilitators. Participants will learn from and connect with physicists, computer scientists, engineers and mathematical scientists who are experts in quantum science. This in-person gathering will be held in fall 2024 in the Washington DC area. A primary deliverable from the convening will be a report summarizing the activities and recommendations generated during the event. Key presentations will be recorded and will be available on a SIAM webpage.

Society for Industrial and Applied Mathematics (SIAM) will host this convening with the goals of (i) making more mathematical scientists aware of the demand for their expertise in quantum research and articulating areas and problems where they can contribute, (ii) increasing the participation of researchers in mathematical sciences in the quantum information science revolution to accelerate its research and development, (iii) providing a seeding ground for partnerships and collaborations of mathematical scientists with physicists, computer scientists, and engineers from industry and academia, and (iv) recommending activities to develop a quantum science and technology workforce pipeline in the mathematical and computational sciences. A few topics in quantum science where mathematics can help research and discovery include quantum computing, quantum algorithms, quantum optimization, quantum error corrections, quantum information theory, quantum cryptography, quantum sensing and metrology, and quantum networks.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2407999","A Symbolic Bifurcation Approach for Complex Deterministic Dynamics","DMS","APPLIED MATHEMATICS","08/01/2024","07/31/2024","Andrey Shilnikov","GA","Georgia State University Research Foundation, Inc.","Continuing Grant","Stacey Levine","07/31/2027","$166,285.00","","ashilnikov@gsu.edu","58 EDGEWOOD AVE NE","ATLANTA","GA","303032921","4044133570","MPS","126600","","$0.00","Many significant advancements in deterministic nonlinear science, crucial for driving progress in cutting-edge engineering, rely heavily on a deeper understanding and practical application of complex theoretical elements borrowed from dynamical systems and bifurcation theory. To realize their full potential in practice, these advances require incorporating mathematical and simulation tools into powerful computing platforms, such as massively parallel and affordable graphics processing units. This project involves the development of new, algorithmically simple, yet efficient and generalizable mathematical approaches for analyzing bifurcations in high-dimensional systems that integrate into intelligent, comprehensive simulations. The goal is to enable quantitative and, more importantly, qualitative progress in higher-level studies of data-driven, detailed, and phenomenologically-reduced models with complex nonlinear dynamics. These models find diverse applications, ranging from engineering and meteorology to living systems, including neural networks. This project also involves interdisciplinary training and educational opportunities for graduate
students, undergraduate students, and high school students, with a particular focus on involving under-represented students in STEM.

The long-term goal of this project is two-fold: to further extend the applied theory of non-local bifurcations and to foster its broader applications. This is expected to lead to a better understanding and demonstration of the universality of the rules of complex dynamics across diverse systems. Homoclinic bifurcations are key to understanding the origin and fine organization structure of deterministic chaos in various systems, including diverse applications found in physics, neuroscience, and economics. A new symbolic approach will be developed which aims to reveal an array of homoclinic and heteroclinic bifurcations in typical systems with complex dynamics due to interactions of saddle equilibria.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2406853","Enhanced Dissipation, Accelerating Langevin Dynamics, and Bose--Einstein Condensation","DMS","APPLIED MATHEMATICS","09/01/2024","07/31/2024","Gautam Iyer","PA","Carnegie-Mellon University","Continuing Grant","Stacey Levine","08/31/2027","$144,902.00","","gautam@math.cmu.edu","5000 FORBES AVE","PITTSBURGH","PA","152133815","4122688746","MPS","126600","","$0.00","Enhanced dissipation arises in many situations of physical importance, ranging from micro fluids to oceanography, and is even commonly observed when cream is poured into coffee and it mixes quickly when stirred but very slowly if left alone. This is the phenomenon by which the combination of stirring and diffusion increases the rate of convergence to equilibrium. This project plans to develop a theoretical understanding of enhanced dissipation, including quantifying this effect and producing criterion describing scenarios where enhanced dissipation occurs at the optimal rate. The methods developed will also be used to speed up sampling algorithms and are useful in scientific computation. In addition to enhanced dissipation, the project also involves the study of the formation of Bose?Einstein condensates in situations which are of interest in modern cosmology. Students and post-docs working on this project will be exposed to a broad set of fundamental tools in partial differential equations, probability, and scientific computation, positioning them to contribute to the ever-changing scientific landscape.

Advection and diffusion are two fundamental phenomena that arise in a wide variety of applications ranging from micro-fluids to meteorology, and even cosmology. In many situations the interaction between advection and diffusion results in an increased rate of convergence to equilibrium -- a phenomenon known as ?enhanced dissipation?. This project involves a quantitative study of enhanced dissipation, obtaining sharp bounds, determining criterion describing scenarios where it occurs at the optimal rate, and investigating its properties. The methods developed can also be used to speed up certain Markov processes and may improve rates of convergence of commonly used Monte Carlo Markov Chain algorithms. In addition to enhanced dissipation, the project will also study the formation of Bose--Einstein condensates in high temperature plasmas. This arises in cosmological applications such as the study of the interaction between matter and radiation in the early universe, the radiation spectra for the accretion disk around black holes. The project aims to classify mechanisms by which condensates form, prove convergence and stability of a numerical scheme, and study condensates in the three-dimensional versions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2408369","Inverse problems from geophysics and transport theory, and applications","DMS","APPLIED MATHEMATICS","08/01/2024","08/01/2024","Hanming Zhou","CA","University of California-Santa Barbara","Standard Grant","Stacey Levine","07/31/2027","$270,000.00","","hzhou@math.ucsb.edu","3227 CHEADLE HALL","SANTA BARBARA","CA","931060001","8058934188","MPS","126600","","$0.00","Seismic tomography plays a central role in our understanding of the substructure of the Earth. The analysis of various seismic data produced by natural earthquakes or artificial seismic sources has important applications in practice, such as characterizing fractured bedrock, and searching for oil and gas deposits. The study of seismology also has a close connection with the transport theory in classical mechanics, which models the behavior of a large number of particles. An essential question in transport theory is to recover the hidden properties of the particles and medium from various physical measurements. This arises in a wide range of applications, including medical imaging, optical tomography, remote sensing, seismology and atmospheric science. This project will address both the theoretical foundations and applications of important challenges arising in seismic tomography and transport theory. The project will provide training opportunities for graduate students, especially those from underrepresented groups.

This project aims to address the applied analysis of several linear and non-linear inverse problems. It contains two major lines of research. The first topic is on the travel time tomography arising in geophysics, which consists of reconstructing seismic sound speed from the travel time of seismic waves propagating through the Earth. The goal is to study the uniqueness and stability of the travel time tomography in anisotropic elasticity, which is essentially the boundary rigidity problem in Finsler geometry. The investigator will also address the uncertainty quantification of the Bayesian inversion method for travel time tomography as well as carry out numerical experiments. The second topic addresses inverse problems for time-dependent transport equations, which concerns the recovery of time-independent or time-dependent coefficients or sources inside a bounded domain from the boundary measurements of the solution to the transport equation. The investigator will study both the theoretical aspects, including the uniqueness and stability estimates, and the applied aspects, such as the reconstruction methods and numerical implementations. The outcomes of the project are likely to lead to new developments on related research topics and techniques, both inside and outside the mathematical community.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -39,14 +41,13 @@ "2424801","Neural Networks for Stationary and Evolutionary Variational Problems","DMS","APPLIED MATHEMATICS","03/01/2024","08/02/2024","Stephan Wojtowytsch","PA","University of Pittsburgh","Continuing Grant","Stacey Levine","07/31/2026","$99,785.00","","s.woj@pitt.edu","4200 FIFTH AVENUE","PITTSBURGH","PA","152600001","4126247400","MPS","126600","079Z","$0.00","Artificial neural networks have become one of the dominant models in data science, used in applications from image classification to natural language processing. Their empirical success in these diverse fields has sparked interest in further applying such models in new directions, such as numerical analysis and scientific computing. This project is aimed at developing a deeper understanding of the capabilities and limitations of the role of neural network models used for numerical analysis and scientific computing, particularly when compared with more classic tools. This is essential in enabling neural network models to be widely deployed in sensitive fields across engineering domains. Graduate students will be trained as part of this project, modern tools from data science and deep learning will be incorporated into graduate curricula, and outreach activities are planned to attract undergraduates as well as underrepresented groups in STEM into this research area.

The focus of this work is on the use of neural network models in numerical algorithms used in models based on the calculus of variations, targeting two case studies. The first is related to functionals that exhibit the Lavrentiev gap phenomena, where an energy gap between the lowest energy achievable by shallow neural networks and more general functions is considered. The second is the Allen-Cahn equation, where the solution strategy of physics-inspired neural networks is analyzed. In the second problem, the adaptivity of neural networks to low-dimensional moving interfaces plays a key role when comparing to e.g. fixed mesh finite element methods. The theoretical results are intended to better understand two fundamental challenges. The first is whether the adaptivity of neural networks can be harnessed for the numerical approximation of spatially very inhomogeneous variational problems. The second seeks to understand the precise situations in which neural network solvers are not expected to outperform traditional solvers.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2407166","Dynamics for sampling: kinetic equations, gradient flows and beyond","DMS","APPLIED MATHEMATICS","08/01/2024","07/31/2024","Lihan Wang","PA","Carnegie-Mellon University","Standard Grant","Hailiang Liu","07/31/2027","$150,000.00","","lihanw@andrew.cmu.edu","5000 FORBES AVE","PITTSBURGH","PA","152133815","4122688746","MPS","126600","","$0.00","Sampling from a target probability distribution is crucial across scientific domains, such as molecular dynamics, statistical physics, Bayesian statistics, and machine learning. The target distribution encodes critical information about systems, such as the likelihood of particle configurations in physical space or parameter choices in large dataset models. Sampling algorithms simulate particle evolution over time, converging to the target distribution after a long time. The PI aims to advance his understanding of the efficiency of these sampling algorithms and enhance their performance, providing useful insights for practitioners. The PI will mentor undergraduate researchers and develop courses on sampling for advanced undergraduate and early-stage graduate students.

Mathematical tools from partial and stochastic differential equations, probability theory, and numerical analysis will be used to study both theoretical and algorithmic aspects of sampling dynamics. Specifically, the project will: (1) develop a framework using functional inequalities, Sobolev spaces, and Markov semigroup theory to analyze long-time convergence properties of sampling dynamics characterized by kinetic equations, and (2) use techniques from optimization, optimal transport, applied analysis, and mean-field limits of interacting particle systems to study sampling dynamics structured as gradient flows, including scenarios where standard gradient flow theory is not directly applicable.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2426456","Conference: Dynamics Days 2025","DMS","APPLIED MATHEMATICS","09/01/2024","07/24/2024","Juan Restrepo","CO","University of Colorado at Boulder","Standard Grant","Hailiang Liu","08/31/2025","$49,893.00","James Meiss","juanga@colorado.edu","3100 MARINE ST","Boulder","CO","803090001","3034926221","MPS","126600","075Z, 079Z, 7556","$0.00","This grant supports the conference ""Dynamics Days US 2025"", which will take place in Denver, Colorado, January 3-5, 2025. Dynamics Days is an annual international conference focused on nonlinear dynamics and its applications that has been running in the US for more than 40 years. The conference will provide a venue for young researchers to present their ideas and learn about cutting-edge results in the field. The conference will have 16 invited speakers, a similar number of contributed talks, and two poster sessions. The majority of the funds will be used to provide travel support to students, postdocs, and other individuals without other sources of support. The participation of students and young researchers from underrepresented groups will be particularly encouraged.

Dynamics Days is one of the premier conferences in nonlinear dynamics in the US, with more than four decades of history. During this time, it has established itself as an excellent venue for the exchange of ideas and results on nonlinear dynamics, chaos, and their applications. The conference is characterized by covering a wide variety of interdisciplinary topics, promoting the cross-fertilization of ideas across disciplines. Topics covered in the conference include networks, fluid dynamics and mixing, data-driven modeling, modeling of complex systems, nonlinear waves, machine learning applications to nonlinear dynamics, and biological systems. Attendees include researchers from physics, mathematics, engineering, and the biological sciences. The conference webpage is www.ddays.org/2025.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2407293","Geometric Problems in Elasticity of Thin Films, Kirigami, and the Monge-Ampere System","DMS","APPLIED MATHEMATICS","08/01/2024","07/24/2024","Marta Lewicka","PA","University of Pittsburgh","Standard Grant","Dmitry Golovaty","07/31/2027","$266,696.00","","lewicka@pitt.edu","4200 FIFTH AVENUE","PITTSBURGH","PA","152600001","4126247400","MPS","126600","","$0.00","The investigator pursues projects that combine questions in mathematical analysis, differential geometry, calculus of variations, materials science and engineering design. The key components are: (i) seeking to determine mechanical theories of thin multi-dimensional films with nonzero stored energy due to shape-formation processes such as growth or plasticity; (ii) the quest for regularity of solutions to a class of partial differential equations arising when the aforementioned prestrained films deform in order to release their energies; (iii) describing properties of ?kirigamized? sheets, namely thin films with cuts of different geometries and distributions. Some of these projects are accessible to graduate students and contribute to their training.

The related analytical projects include: (i) dimension reduction in nonlinear elasticity of prestrained materials, in function of the general prestrain given by a Riemannian metric, Gamma-convergence and rigidity estimates; (ii) convex integration and flexibility in the Holder regularity classes for the Monge-Ampere system and the k-Hessian system; and (iii) investigating structure and rectifiablity of geodesics in the kirigamized sheets in relation to the sheet?s deployment trajectory. ?

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2407033","Novel Model Development for Material Systems: Data-driven Algorithms and Interacting Particle Methods","DMS","APPLIED MATHEMATICS","08/01/2024","05/16/2024","Karl Glasner","AZ","University of Arizona","Continuing Grant","Dmitry Golovaty","07/31/2027","$187,593.00","","kglasner@math.arizona.edu","845 N PARK AVE RM 538","TUCSON","AZ","85721","5206266000","MPS","126600","","$0.00","Models for complex materials have traditionally relied on a mixture of physical understanding along with phenomenological guesswork. This project seeks new avenues for model building, incorporating advances in machine learning and novel mathematical paradigms. Experimental and simulation data is combined with physical laws to determine the structure of model equations, leading to more realistic descriptions of physical systems, enhanced prediction ability, and reconstruction of noisy and missing data. A second aim is the development of models involving interacting agents that mimic physical processes. These will be utilized for large scale computations that are currently infeasible. Graduate student training is an integral part of the project.

This project investigates new approaches to construct and simulate models in material systems. Regression algorithms are developed for simultaneous parameter and state inference and discovery for partial differential equations, utilizing either experimental data or detailed numerical simulations. These will be used for applications in complex polymer systems, phase field models, model reduction, and reconstruction of materials data. Energy driven models of interacting particles and their mean-field limits are investigated using numerical simulation along with formal and rigorous analysis. Connections with phase-separation, nematic and self-assembling pattern-formation phenomenon are established, and allow for Lagrangian numerical methods that utilize coarse-grained interaction potentials. Project results can be adapted to a vast array of physical and biological models, and can serve as tools for data analysis and assimilation.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2408793","Anisotropic Inverse Problems: Nonlocality, Nonlinearity, and High Frequencies","DMS","APPLIED MATHEMATICS","07/01/2024","05/14/2024","Katya Krupchyk","CA","University of California-Irvine","Standard Grant","Stacey Levine","06/30/2027","$270,000.00","","katya.krupchyk@uci.edu","160 ALDRICH HALL","IRVINE","CA","926970001","9498247295","MPS","126600","","$0.00","Inverse problems arise when measurements obtained from the exterior or boundary of a medium are employed to unveil the properties of its inaccessible interior. This framework is ubiquitous across various scientific and technological disciplines, encompassing fields such as medical imaging, atmospheric remote sensing, geophysics, and non-destructive evaluation. In many practical scenarios, medium parameters exhibit anisotropy, meaning they depend not only on position but also on direction. Examples include conductivity in muscle tissue in human bodies, electromagnetic parameters in crystals, composite materials like fiber-reinforced polymers, and seismic wave propagation in the Earth. The project aims to develop novel mathematical methods for investigating inverse problems related to the recovery of anisotropic medium parameters from measurements taken at the exterior or boundary. A particular focus of the project is on determining parameters in models involving long-range interactions, prevalent in phenomena from anomalous diffusion to random processes with jumps, with broad applications spanning image processing, fluid dynamics, biophysics, network science, epidemiology, and finance. Additionally, the project places significant emphasis on providing educational training for graduate students.

The project leverages nonlocality, nonlinearity, and high frequencies as powerful tools to tackle significant and challenging inverse problems in anisotropic media. It is organized around four pivotal research topics. The first topic concerns inverse problems for elliptic partial differential operators at a large but fixed frequency. The goal is to solve important inverse problems for both linear and nonlinear elliptic operators at a large but fixed frequency in a geometric setting where the corresponding inverse problems at zero frequency are wide open and seem difficult to reach. The second topic focuses on inverse problems for nonlocal elliptic operators, with a particular emphasis on the fractional counterpart of the Calderon problem. The aim is to recover the coefficients of nonlocal operators based on measurements taken in exterior regions. The inherent nonlocality of these operators renders inverse problems more tractable than their local counterparts. The third topic deals with inverse problems for significant nonlinear hyperbolic and elliptic partial differential equations, encountered in physical models. The primary objective is to recover the leading terms that govern the underlying geometry. Finally, the fourth topic addresses inverse problems for both linear and nonlinear perturbations of biharmonic operators, with applications ranging from elasticity theory to conformal geometry.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2433859","Conference: 1st SIAM Northern and Central California Sectional Conference","DMS","APPLIED MATHEMATICS, COMPUTATIONAL MATHEMATICS","09/01/2024","07/25/2024","Noemi Petra","CA","University of California - Merced","Standard Grant","Hailiang Liu","08/31/2025","$40,000.00","Changho Kim, Erica Rutter, Boaz Ilan, Roummel Marcia","npetra@ucmerced.edu","5200 N LAKE RD","MERCED","CA","953435001","2092012039","MPS","126600, 127100","075Z, 079Z, 7556, 9263","$0.00","The Society for Industrial and Applied Mathematics (SIAM) recently recognized the establishment of the Northern and Central California (SIAM-NCC) Section, whose primary goal is to provide an ongoing opportunity for mathematicians working in the sectors of academia, national laboratory, industry, and government to come together and form a strong social and professional network. The first SIAM-NCC conference scheduled to be held at the University of California, Merced campus during October 9-11, 2024 has the following aims: (1) create an opportunity for scientific researchers in the central and northern California regions to meet, network, and share the innovations and recent developments in their fields; (2) attract and energize a diverse group of students and researchers particularly those from underrepresented minority groups; (3) offer opportunities to SIAM members from various institutions in the region to present their work, who for various reasons often struggle to participate at national and international SIAM meetings; and (4) provide early career researchers to connect with others who are at similar career stages. The broader goal of this conference is to bring together a diverse group of students and researchers particularly those from underrepresented minority groups and create opportunities for sharing ideas and networking. The central and northern California regions provide rich opportunities for involving students from underrepresented and financially challenged populations majoring in science, technology, engineering, and mathematics (STEM) fields.

The 2024 SIAM-NCC Conference is centered around the following five research themes of applied mathematics: (1) mathematical and numerical analysis; (2) optimization, inverse problems, and optimal experimental design; (3) scientific and high-performance computing; (4) uncertainty quantification and prediction; and (5) scientific machine learning (ML), artificial intelligence (AI), and digital twins. The conference will feature four plenary speakers from industry, academia, and national laboratory. Ten mini-symposia are planned to capture the conference themes in critical areas of research in applied mathematics. Four panels will cover a variety of topics aimed to reach undergraduate and graduate students, early career researchers, and the greater scientific community. In particular, topics include (1) career opportunities for undergraduate students, (2) transitioning from student to researcher (e.g., preparing for internships and postdoc positions), (3) industry and laboratory careers, and (4) the role of AI/ML in science and technology. Finally, to facilitate a more open and informal discussion about research and career opportunities, to accommodate broader research themes, and to offer opportunity for all attendees to present their work, two poster sessions are also scheduled. Undergraduate and graduate students, as well as postdoctoral scholars and other early career researchers, will be particularly encouraged to participate in these sessions. The conference website is: https://sites.google.com/view/siam-ncc/siam-ncc-conference-2024.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2407080","Soliton Gases for the Focusing Nonlinear Schroedinger Equation and Other Integrable Systems: Theory and Applications","DMS","APPLIED MATHEMATICS","09/01/2024","05/15/2024","Alexander Tovbis","FL","The University of Central Florida Board of Trustees","Continuing Grant","Dmitry Golovaty","08/31/2027","$172,211.00","","alexander.tovbis@ucf.edu","4000 CENTRAL FLORIDA BLVD","ORLANDO","FL","328168005","4078230387","MPS","126600","","$0.00","Nonlinear integrable equations play increasingly important role in the modelling of various phenomena in natural sciences and engineering. This fact stems from two key observations: a) these equations can capture various physical phenomena that cannot be described by simpler models, and b) these equations allow for various classes of solutions that can be calculated in explicit form. For example, the Nonlinear Schroedinger Equation (NLS), is widely used to model wave propagation in weakly nonlinear dispersive media (fiber optics, deep water gravity waves) when dissipation can be neglected. It was observed that solitons, which are the most celebrated explicit solutions of integrable systems, can be viewed as ?""quasi particles"" of complex statistical objects called soliton gases. The main idea of this project is to model random nonlinear waves, which are frequently encountered in natural phenomena, with large random ensembles of solitons. Ultimately, the project aims to enhance our ability to predict and, in some cases, to control random nonlinear waves, as well as to derive their statistical characteristics. Being by nature a mixture of pure and applied mathematics and also leading to new lab experiments, the work on the project could benefit by cross pollination of ideas and methods originating from different parts of nonlinear waves research community. The project is expected to advance our general knowledge of random nonlinear waves, including the rogue waves (RW), and to improve methods of prediction of the latter. In the fiber optics, the results of the project may help to model and, perhaps, to control the evolution of noise in NLS governed nonlinear fibers. The project will also serve as a vehicle for training graduate and undergraduate students, including minorities, as well as postdocs.

The main goals of this project are a) development of a rigorous spectral theory for soliton gases for integrable equations (KdV, fNLS, sine-Gordon, etc.), and b) statistical characterization of such soliton gases. The work in part a) requires rigorous derivation and analysis of the nonlinear dispersion relations (NDR), which describe spectral characteristics of the gases, as well as construction of explicit families of solutions to NDR (condensates, periodic gases, etc.) that can be of special interest in applications. The recent observation by the principal investigator (PI) that the NDR can be considered as a large genus (``thermodynamic"") limit of Riemann Bilinear Identities on some special sequences of Riemann surfaces reveals a deep and intriguing connections between the algebraic geometry and the spectral theory of soliton gases for integrable equations, which the PI is interested in understanding and analyzing. This approach requires some new potential theory methods for solving minimization problems on Riemann surfaces. Calculation of important statistical characteristics (probability density function, power spectrum, kurtosis, etc.) of the soliton gases from part b) contains both analytical and numerical components. The obtained theoretical results will lead to laboratory experiments in collaboration with leading experts in the area of experimental fiber optics and water waves.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405326","Hydrodynamic Theory of Environmental Averaging and Self-organization","DMS","APPLIED MATHEMATICS","06/01/2024","05/15/2024","Roman Shvydkoy","IL","University of Illinois at Chicago","Standard Grant","Pedro Embid","05/31/2027","$280,000.00","","shvydkoy@uic.edu","809 S MARSHFIELD AVE M/C 551","CHICAGO","IL","606124305","3129962862","MPS","126600","","$0.00","Many mathematical models of swarming behavior reflect the tendency of every agent to adjust its velocity to an averaged direction of motion of the crowd around. Such examples are abundant in biology, dynamics of human crowds, social networking, and even in technology (coordinated fight of an escort of UAVs or satellite navigation). Although the laws that describe the average may not be given explicitly, most adhere to a few basic principles. First, agents react more to the closest neighbors, and second, the density of the swarm plays a constructive role in defining particular communication rules. Such rules give rise to what is called ""environmental averaging"". Large swarms regulated by environmental averaging are governed by models similar to those we use to study motion of a liquid like water or gas. Thanks to this connection a new trend emerged in the studies of collective behavior which looks at these phenomena from the point of view of hydrodynamic modeling. This project proposes to analyze hydrodynamic collective models aiming at understanding their fundamental mathematical properties and with a view towards their applications to collective phenomena. In parallel with the research effort, the project will involve students and researchers through a working group seminar on the mathematics of collective behavior at the University of Illinois at Chicago.

Central to the project will be the development of a general methodology that unifies numerous models. Focus will be placed on justification of a class hydrodynamic models called Euler Alignment System and its kinetic counterpart the Fokker-Planck-Alignment model. We aim to provide a justification for such systems going from particle dynamics through the mean-field limit and into macroscopic description through various hydrodynamic limits. It will be possible to obtain new barotropic pressure laws which have proved to be useful in real life modeling. Exploiting parallels with the classical theory of fluids we plan to study collective outcomes described by natural thermodynamic equilibria of the system, and to bring the regularity theory of such systems to the level usable in the studies of long-time behavior of the system. Applications of this research are numerous including opinion mean-field games, segregation modeling, and modeling of turbulent phenomena in 2D inviscid fluids.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2407550","Collaborative Research: Stochastic Modeling for Sustainable Management of Water Rights","DMS","APPLIED MATHEMATICS","07/01/2024","05/21/2024","Michael Ludkovski","CA","University of California-Santa Barbara","Standard Grant","Pedro Embid","06/30/2027","$220,000.00","","ludkovski@pstat.ucsb.edu","3227 CHEADLE HALL","SANTA BARBARA","CA","931060001","8058934188","MPS","126600","124Z, 5294","$0.00","Sustainable and equitable management of groundwater is one of the key aspects of adaptation to climate change in drought-affected regions nationwide. The rapid depletion of aquifers is spurring the creation of new groundwater management institutions to ensure conservation of groundwater supplies across generations. This project will provide new mathematical tools for designing efficient and fair water markets, that are free of predatory or exploitative behavior and flexibly respond to stakeholder needs, helping to build a water resilient future. The developed numerical algorithms would facilitate better market regulations and policies, supporting legislative mandates and their economic viability. The dissemination activities will enhance the exchange of ideas and knowledge between mathematicians, data scientists, resource economists and hydrologists. This award will also provide opportunities for student involvement in the research.

This project will address dynamic water allocation and equilibrium for tradeable water rights by establishing the foundations for an innovative mathematical framework for water management through the lens of stochastic games and market equilibria. The project will develop a tractable top-down stochastic model of groundwater levels to study the price formation of the groundwater rights as a Nash equilibrium of a non-cooperative game between the economic agents. In tandem, the project will characterize the Pareto optimal water rights allocation and water banking strategy from the perspective of a central planner. Modeling and pricing of groundwater rights and their fair distribution will articulate the benefits and dangers of potential management policies and quantify the efficiency of regulations. The project will also develop scalable computational schemes for multi-period equilibria with multiple stakeholders.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2339240","CAREER: Learning Theory for Large-scale Stochastic Games","DMS","APPLIED MATHEMATICS","02/01/2024","01/29/2024","Renyuan Xu","CA","University of Southern California","Continuing Grant","Stacey Levine","01/31/2029","$85,749.00","","renyuanx@usc.edu","3720 S FLOWER ST FL 3","LOS ANGELES","CA","90033","2137407762","MPS","126600","079Z, 1045","$0.00","In modern financial markets and economic systems with large populations, decision-making has evolved into a multifaceted process involving various aspects such as population heterogeneity, diverse information structures, and human-AI interactions. This project aims to develop new learning frameworks and mathematical foundations that strengthen our understanding of the stability, efficiency, and fairness of societal systems with large populations. Novel frameworks developed in this research are designed to have flexible model assumptions, be able to learn from incomplete information, and accommodate heterogeneous risk preferences as well as information asymmetry. This research will involve both undergraduate and graduate students, emphasizing cross-disciplinary training in mathematics and machine learning. Additionally, an outreach program will be established to engage underrepresented groups in STEM.

This project places at its core the mathematical advancement of machine learning theory for stochastic systems with many interacting agents, known as ?mean-field games?. The first goal is to develop new mathematical models and learning algorithms for mean-field games under structural properties such as graphon interactions or additional summary statistics of the population distribution. This development relies on new approximation schemes and stability analyses based on the local propagation of flows. The second goal focuses on principal-agent problems, where agents have diverse risk preferences or the capability to acquire new information. These topics pose significant challenges in a dynamic setting, leading to a novel class of stochastic partial differential equations that require new developments for well-definedness and regularity theory. The final goal focuses on constructing generative models (simulators) with interactive mean-field agents, addressing the scalability issue in agent-based simulator literature. To leverage the computational power of neural networks, a key objective is to establish a universal approximation theorem in the distributional sense and the convergence of an iterative deep-learning scheme to train the simulator.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2407550","Collaborative Research: Stochastic Modeling for Sustainable Management of Water Rights","DMS","APPLIED MATHEMATICS","07/01/2024","05/21/2024","Michael Ludkovski","CA","University of California-Santa Barbara","Standard Grant","Pedro Embid","06/30/2027","$220,000.00","","ludkovski@pstat.ucsb.edu","3227 CHEADLE HALL","SANTA BARBARA","CA","931060001","8058934188","MPS","126600","124Z, 5294","$0.00","Sustainable and equitable management of groundwater is one of the key aspects of adaptation to climate change in drought-affected regions nationwide. The rapid depletion of aquifers is spurring the creation of new groundwater management institutions to ensure conservation of groundwater supplies across generations. This project will provide new mathematical tools for designing efficient and fair water markets, that are free of predatory or exploitative behavior and flexibly respond to stakeholder needs, helping to build a water resilient future. The developed numerical algorithms would facilitate better market regulations and policies, supporting legislative mandates and their economic viability. The dissemination activities will enhance the exchange of ideas and knowledge between mathematicians, data scientists, resource economists and hydrologists. This award will also provide opportunities for student involvement in the research.

This project will address dynamic water allocation and equilibrium for tradeable water rights by establishing the foundations for an innovative mathematical framework for water management through the lens of stochastic games and market equilibria. The project will develop a tractable top-down stochastic model of groundwater levels to study the price formation of the groundwater rights as a Nash equilibrium of a non-cooperative game between the economic agents. In tandem, the project will characterize the Pareto optimal water rights allocation and water banking strategy from the perspective of a central planner. Modeling and pricing of groundwater rights and their fair distribution will articulate the benefits and dangers of potential management policies and quantify the efficiency of regulations. The project will also develop scalable computational schemes for multi-period equilibria with multiple stakeholders.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2306379","Collaborative Research: On New Directions for the Derivation of Wave Kinetic Equations","DMS","APPLIED MATHEMATICS","09/01/2024","03/15/2024","Minh-Binh Tran","TX","Texas A&M University","Standard Grant","Pedro Embid","08/31/2027","$145,000.00","","minhbinh@tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","126600","","$0.00","The beauty and power of mathematics is to recognize common features in a variety of phenomena that may look physically different. This is certainly the case when one studies wave turbulence theory. This theory is focused on the fundamental concept that when in a given physical system a large number of interacting waves are present, the description of an individual wave is neither possible nor relevant. What becomes important and practical is the description of the density and the statistics of the interacting waves. Arguably the most recognizable and fundamental objects within this theory are the wave kinetic equations. These equations, their solutions and their approximations have been used to study a variety of phenomena: water surface gravity and capillary waves, inertial waves due to rotation and internal waves on density stratifications, which are important in the study of planetary atmospheres and oceans; Alfvén wave turbulence in solar wind; planetary Rossby waves, which are important for the study of weather and climate evolutions; waves in Bose-Einstein condensates (BECs) and in nonlinear optics; waves in plasmas of fusion devices; and many others. This project will tackle foundational questions in wave turbulence theory through rigorous mathematical analysis. In addition, the project will promote collaborations, facilitate the dissemination of interdisciplinary research, and provide opportunities for undergraduate and graduate students to work on a multifaceted and forward-looking line of mathematical research.

This project tackles challenging problems at the intersection of the physics and the mathematical analysis of nonlinear interactions of waves that are central in the study of wave turbulence theory. These problems include the rigorous derivation of wave kinetic equations, the analysis of the 4-wave kinetic equation for the Fermi- Pasta-Ulam-Tsingou (FPUT) chain and the well-posedness of a geometric wave equation via Feynman diagrams in the energy regime. The research proposed will not just address important open problems but will contribute to the interdisciplinary development of several new and complex tools both in mathematics and physics. The proposal aims at providing these tools by blending Feynman diagrams, harmonic analysis, probability, combinatorics, incidence geometry, kinetic theory, dispersive PDE, quantum field theory and the FPUT chain.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2337666","CAREER: Well-posedness and long-time behavior of reaction-diffusion and kinetic equations","DMS","APPLIED MATHEMATICS","06/01/2024","01/22/2024","Christopher Henderson","AZ","University of Arizona","Continuing Grant","Pedro Embid","05/31/2029","$31,477.00","","ckhenderson@math.arizona.edu","845 N PARK AVE RM 538","TUCSON","AZ","85721","5206266000","MPS","126600","1045, 9251","$0.00","This project focuses on the behavior of physical, chemical, and biological systems that can be modelled by partial differential equations (PDEs). The forces that determine the time-evolution of these systems are complex, making their analysis subtle and technical. Two fundamental questions of interest are the qualitative behavior of these systems, e.g., whether solutions have large fluctuations, and their long-time behavior, e.g., by quantifying the speed with which an invasive species overruns a new environment. These questions are interdependent, with the latter relying on an understanding of the former. Our ability to understand the long-time behavior of PDE, including identifying the key quantities on which each long-time outcome depends, allows us to predict the behavior of real-world systems in a way that cannot be captured purely by numerical simulation, which, by necessity, is restricted to finite time scales. This project will develop novel methods for these goals. Graduate and undergraduate research will be integrated into the project, training the next generation of applied mathematicians and scientists. The project also involves a summer boot camp for entering applied mathematics PhD students transitioning from adjacent, but nonmathematical, fields that shore up their mathematical reasoning (logical thinking) and technical writing skills. Their training is impactful because these students have diverse interests (mathematical biology, machine learning, data science, PDE and numerical analysis, etc.) and go on to careers in industry, academia, and national labs.

This project focuses on advances in reaction-diffusion equations and collisional kinetic equations. In the former, the project will develop a novel ""Stein's method"" approach to PDE that is based on the observation that monotonic steady states of a given PDE satisfy first order autonomous ordinary differential equations (ODE) and that, to show convergence of a generic solution of the PDE to such a steady state, it is enough to show that the generic solution converges to a solution of the ODE. The research will leverage new functional inequalities and ideas in the calculus of variations. In the latter, the project will import techniques from parabolic theory and stochastic analysis to characterize when blow-up occurs in generic domains (both with and without boundaries). This requires the precise and quantitative understanding of the regularity of solutions near the boundary in physical space and the decay of solutions at ""large"" velocities.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2340631","CAREER: Solving Estimation Problems of Networked Interacting Dynamical Systems Via Exploiting Low Dimensional Structures: Mathematical Foundations, Algorithms and Applications","DMS","APPLIED MATHEMATICS, COMPUTATIONAL MATHEMATICS","09/01/2024","02/02/2024","Sui Tang","CA","University of California-Santa Barbara","Continuing Grant","Stacey Levine","08/31/2029","$241,397.00","","suitang@math.ucsb.edu","3227 CHEADLE HALL","SANTA BARBARA","CA","931060001","8058934188","MPS","126600, 127100","079Z, 1045, 9263","$0.00","Networked Interacting Dynamical Systems (NetIDs) are ubiquitous, displaying complex behaviors that arise from the interactions of agents or particles. These systems have found applications in diverse fields, including ecology, engineering, and social sciences, yet their high-dimensional nature makes them challenging to study. This often leads to significant theoretical and computational difficulties, known as the ?curse of dimensionality.? Recent advances in applied mathematics have shed light on these complexities, revealing that complex NetID patterns can arise from low dimensional interactions. Building on these insights, this project is dedicated to developing a theoretical and computational framework to address the estimation problems within these models by exploiting the underlying low dimensional structures. The overarching goal is to create efficient, physically interpretable surrogate models that bridge the gap between qualitative analysis and quantitative data-driven applications, ranging from sensor network optimization to modeling the environmental and climate impacts on fish migration. This research program will provide research opportunities for both undergraduate and graduate students, featuring a graduate summer school at the intersection of NetIDs and machine learning. There will be a particular focus on engaging female and underrepresented minority students in this vibrant field, blending machine learning with differential equations. The project's findings will also enrich mathematical data science course materials for both undergraduate and graduate education.

This project aims to make fundamental mathematical, statistical, and computational advances for solving NetIDs' estimation problems. The research will focus on three primary areas: (1) Developing innovative sampling strategies for optimal data recovery in NetIDs with linear interactions by exploiting their inherent low-dimensionality in terms of sparsity, smoothness, low-rankness. (2) Establishing robust statistical estimation of NetIDs with nonlinear time-varying interactions by combining machine learning, numerical analysis, and functional data analysis to create physically consistent estimators that bypass the ?curse of dimensionality,? while exploring the identifiability and convergence as sample sizes increase. (3) Investigating the statistical predictive properties of Graph Neural Differential Equations, aiming to derive upper bounds for their transferability and generalization error. The results of this project are expected to address the computational challenges of large-scale Graph Neural Networks and bridge theory and practice in NetIDs research.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." diff --git a/Combinatorics/Awards-Combinatorics-2024.csv b/Combinatorics/Awards-Combinatorics-2024.csv index 006377a..022f2f9 100644 --- a/Combinatorics/Awards-Combinatorics-2024.csv +++ b/Combinatorics/Awards-Combinatorics-2024.csv @@ -1,7 +1,10 @@ "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract" +"2435236","Conference: The KOI Combinatorics Lectures","DMS","Combinatorics","09/01/2024","08/19/2024","Mihai Ciucu","IN","Indiana University","Continuing Grant","Stefaan De Winter","08/31/2027","$15,260.00","Margaret Readdy, Richard Ehrenborg, Eric Katz, Saul Blanco Rodriguez","mciucu@indiana.edu","107 S INDIANA AVE","BLOOMINGTON","IN","474057000","3172783473","MPS","797000","7556","$0.00","The 3rd KOI Combinatorics Lectures will be held October 4-5, 2024 at Indiana University. This regional conference is organized by members of the combinatorics community from the Kentucky, Ohio and Indiana (KOI) area. It seeks to rebuild and initiate research connections among the KOI area graduate students, postdocs and faculty, including individuals from over thirty nearby small colleges, regional universities and ethnically diverse colleges. The conference program consists of four talks from emerging and established researchers in combinatorics broadly defined, a problem session, and a poster session that is open to all participants. In Japanese culture, koi symbolize strength, courage, patience and success through perseverance. All of the conference activities serve to strengthen these attributes among the participants, with a strong focus on increasing the numbers of underrepresented groups in the mathematical sciences, including women. The follow-up yearly conferences will continue at the University of Kentucky in 2025 and the Ohio State University in 2026.


The KOI Combinatorics Lectures showcase national and internationally recognized researchers in combinatorics. New developments in combinatorics and its interactions with other mathematical fields including algebraic geometry, algebra, topology, and artificial intelligence, will be featured. Interactions among all of the participants and the speakers, as well as learning the latest progress and techniques in the field of combinatorics, have the potential to contribute to the growing connections between combinatorics and other scientific areas, including physics, computer science and biology. The vertical mentoring, inclusion of educational activities, and recruitment of speakers and participants from a broad range of institutions and backgrounds contribute to the engagement, retention and equity goals of the NSF. Further details about the conference may be found on the website https://sites.google.com/view/koicombinatorics/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2349088","RUI: Combinatorial Models in Representation Theory, Geometry, and Analysis","DMS","Combinatorics","09/01/2024","08/19/2024","Julianna Tymoczko","MA","Smith College","Standard Grant","Stefaan De Winter","08/31/2027","$210,000.00","","jtymoczko@smith.edu","10 ELM ST","NORTHAMPTON","MA","010636304","4135842700","MPS","797000","","$0.00","Graphs are essential tools used to model and analyze networks of all kinds: digital, electrical, social, epidemiological, etc. In many applications, the edges of a graph are labeled with additional data that indicates the capacity of the edge. The PI seeks to optimize some aspect of the graph depending on the application. For instance, if the edge labels of a subway map indicate the capacity of each line at different times of day, one might want to maximize the total number of passengers that can be transported between two stations during rush hour; while if the edge labels of a road map indicate cost to plow the road, one might want to minimize the cost to plow paths between all essential services. This project analyzes two kinds of edge-labeled graphs: webs, which arise in knot theory and representation theory as well as combinatorics; and algebraic splines, which arise in analysis and applied math, especially in data compression or data interpolation. Undergraduate students and postdocs will be involved in the project.

Previous constructions of webs rely on local information about edge-labelings and seek to identify global properties (including bases of the associated representation, or coefficients in a knot-theoretic state sum). With Russell, the PI proposes a new model of webs called ''stranding'' that identifies many of these global properties as paths through the graph. This unlocks exciting and promising new attacks on open questions in the field. In splines, the PI will develop and expand on recent progress with Nazir and Schilling towards the longstanding lower bound conjecture for the dimension of splines. Simultaneously, the PI continues projects to analyze a special family of splines that model equivariant cohomology, with applications towards the Stanley-Stembridge conjecture in algebraic combinatorics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2349013","Local to Global Phenomena in Extremal and Probabilistic Combinatorics","DMS","Combinatorics","09/01/2024","08/19/2024","Matija Bucic","NJ","Princeton University","Standard Grant","Stefaan De Winter","08/31/2027","$210,001.00","","matija.bucic@ias.edu","1 NASSAU HALL","PRINCETON","NJ","085442001","6092583090","MPS","797000","","$0.00","This project will focus on the local-to-global principle, a fascinating phenomenon occurring across mathematics, computer science, and beyond. At a very general level the local-to-global principle states that one can obtain global understanding of a structure from having a good understanding of its local properties or vice versa. In this project, we will focus on exploring local-to-global phenomena in extremal and probabilistic combinatorics with a particular focus on finding applications of local-to-global ideas to a wide variety of central open problems in discrete mathematics and beyond. The project will offer hands-on research opportunities for graduate students, contributing to their training and potentially leading to the integration of findings into graduate-level courses.

More specifically the project will focus on three seemingly distant central open problems in the area. The first one is the Erd?s-Gallai Conjecture asserting that every graph can be decomposed into just linearly many cycles and edges. The second one is Rota's Basis Conjecture, which asserts that given any n bases in a matroid we can find n disjoint transversal bases. The third is the Erd?s Unit Distance Problem asking for the maximum number of unit distances defined by n points in the plane. While at a surface level, these three problems ranging from graph and matroid theory to discrete geometry may seem very different, recent work involving sublinear expansion provided very surprising common threads. With this in mind, the project aims to further develop the theory of sublinear expander graphs, one of the most prolific recent local-to-global ideas in discrete mathematics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348785","Polyhedral Subdivisions in Combinatorics and Geometry","DMS","Combinatorics","08/15/2024","08/14/2024","Xue Liu","WA","University of Washington","Continuing Grant","Stefaan De Winter","07/31/2026","$61,045.00","","gakuliu@uw.edu","4333 BROOKLYN AVE NE","SEATTLE","WA","981951016","2065434043","MPS","797000","","$0.00","This project will study polyhedral subdivisions and their applications to different areas of mathematics. Polyhedra are higher dimensional versions of polygons. They include cubes, pyramids, prisms, and many other shapes. These objects have been studied since antiquity. Gluing polyhedra together forms polyhedral complexes, which are ubiquitous throughout mathematics, computer science, and engineering. For example, polyhedral complexes are used to subdivide a space into smaller, more manageable pieces. This research aims to further our fundamental understanding of these objects and will include the involvement of students.

Three specific problems that will be looked at are: (1) Spaces of subdivisions and the Baues conjecture: examining how well certain combinatorially defined spaces can approximate moduli spaces from geometry. (2) Unimodular triangulations and lattice polytopes: the existence and construction of unimodular triangulations, and their applications to resolutions of singularities in algebraic geometry. (3) Hadwiger's covering problem, as seen through the lens of subdivisions, and applications to convex geometry. The PI plans to develop new tools to help strengthen the interplay between combinatorics, geometry, and topology.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2444020","Combinatorics of Total Positivity: Amplituhedra and Braid Varieties","DMS","Combinatorics","09/01/2024","08/12/2024","Melissa Sherman-Bennett","CA","University of California-Davis","Standard Grant","Stefaan De Winter","08/31/2027","$180,000.00","","msherben@mit.edu","1850 RESEARCH PARK DR STE 300","DAVIS","CA","956186153","5307547700","MPS","797000","","$0.00","The answers to real world problems, such as determining the behavior of particles in particle accelerators, are often quite complicated. Mathematics abstracts these complicated behaviors, and often reveals hidden structures; abstraction allows one to see the forest rather than the trees. For example, physicists Arkhani-Hamed and Trnka uncovered a high-dimensional mathematical object called the ""amplituhedron"" whose geometry should govern particle scattering. However, as abstraction increases, intuition decreases; it is easy to lose sight of the trees among the clouds. Algebraic combinatorics, as a mathematical discipline, is a tool to represent abstract mathematics in a more concrete way--similar to how a bar graph or scatter plot is a tool to represent a long list of numbers in a more intuitive way. In the case of the amplituhedron, combinatorics provides a way to break the amplituhedron up into smaller, simpler pieces. It also provides a way to visualize each piece, even though the pieces do not fit in three dimensions. It is through this combinatorics that the conjectural relationship between the amplituhedron and particle scattering is most apparent. In one project the PI will work to prove this conjectural relationship with collaborators Even-Zohar, Lakrec, Parisi, Tessler, and Williams. In general, the PI will seek to better understand the combinatorics of amplituhedra and related mathematical objects called cluster varieties. The PI will involve both undergraduate and graduate students in thisd research.

The broader mathematical context for the proposed projects is the theory of total positivity. Classically, a matrix is totally positive if all minors are positive. Lusztig extended the notion of total positivity to partial flag varieties, while Postnikov independently defined the positive Grassmannian. The combinatorics of total positivity is incredibly rich, leading to the definition of cluster algebras by Fomin and Zelevinsky. The PI proposes to study two generalizations of total positivity through a combinatorial lens. The first project concerns amplituhedra, which generalize the positive Grassmannian and arise in particle physics. The PI will work to resolve conjectures on the relationship between tilings of m=4 amplituhedra and the computation of scattering amplitudes, as well as various conjectures on tilings of m=2 amplituhedra. The second project concerns cluster structures on braid varieties, which generalize positive partial flag varieties. The PI will further develop the combinatorics of this cluster structure, investigating 3D plabic graphs and their relationship to weaves, and explore applications.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2347832","NSF-BSF : Ramsey and Pseudorandom Graph Theory","DMS","Combinatorics","08/15/2024","08/13/2024","Jacques Verstraete","CA","University of California-San Diego","Continuing Grant","Stefaan De Winter","07/31/2028","$190,779.00","","jverstraete@ucsd.edu","9500 GILMAN DR","LA JOLLA","CA","920930021","8585344896","MPS","797000","","$0.00","This proposal concerns research in combinatorics, focusing on a new approach involving pseudorandomness. The general philosophy is that rich structures hide inside pseudorandom combinatorial structures, such as graphs and hypergraphs, and can be found using a combination of spectral, geometric and probabilistic methods. Motivation for their study comes from striking connections and applications to algorithms, coding theory, finite geometry, information theory and cryptography. Their study has led to major breakthroughs on decades-old problems, and in particular in Ramsey Theory, which is underpinned by the qualitative statement that in any sufficiently large combinatorial structure, a relatively large uniform substructure must exist. The new approach marks a shift in focus and direction, away from purely random objects to pseudorandom objects, and leads to exciting questions relative to explicit constructions of codes and algorithms for finding the sought-after structures. This project will provide research training opportunities for students.

Pseudorandom graphs and hypergraphs are central to an area known broadly as extremal combinatorics, and have a richly developed theory over the last few decades. The main idea is to define deterministic properties of a combinatorial structure which force it to behave in many ways similarly to a purely random object. The author and co-researchers discovered in recent work that interesting extremal and Ramsey graphs appear inside pseudorandom graphs, in the sense that a simple random sample tends to produce such graphs. This leads to the solution to classical mathematical problems, some of which have been studied for almost a century, such as the growth of Ramsey numbers. An interesting line of questioning is whether such objects can be constructed without randomness, for instance the promising approach that an exponential construction for diagonal Ramsey numbers could be found by sampling from suitable pseudorandom graphs. This project will develop a deeper analysis of these questions using a broad variety of mathematical tools, including probabilistic and polynomial methods and finite geometric and spectral methods, in order to tackle the most central and important problems in the area.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2444020","Combinatorics of Total Positivity: Amplituhedra and Braid Varieties","DMS","Combinatorics","09/01/2024","08/12/2024","Melissa Sherman-Bennett","CA","University of California-Davis","Standard Grant","Stefaan De Winter","08/31/2027","$180,000.00","","msherben@mit.edu","1850 RESEARCH PARK DR STE 300","DAVIS","CA","956186153","5307547700","MPS","797000","","$0.00","The answers to real world problems, such as determining the behavior of particles in particle accelerators, are often quite complicated. Mathematics abstracts these complicated behaviors, and often reveals hidden structures; abstraction allows one to see the forest rather than the trees. For example, physicists Arkhani-Hamed and Trnka uncovered a high-dimensional mathematical object called the ""amplituhedron"" whose geometry should govern particle scattering. However, as abstraction increases, intuition decreases; it is easy to lose sight of the trees among the clouds. Algebraic combinatorics, as a mathematical discipline, is a tool to represent abstract mathematics in a more concrete way--similar to how a bar graph or scatter plot is a tool to represent a long list of numbers in a more intuitive way. In the case of the amplituhedron, combinatorics provides a way to break the amplituhedron up into smaller, simpler pieces. It also provides a way to visualize each piece, even though the pieces do not fit in three dimensions. It is through this combinatorics that the conjectural relationship between the amplituhedron and particle scattering is most apparent. In one project the PI will work to prove this conjectural relationship with collaborators Even-Zohar, Lakrec, Parisi, Tessler, and Williams. In general, the PI will seek to better understand the combinatorics of amplituhedra and related mathematical objects called cluster varieties. The PI will involve both undergraduate and graduate students in thisd research.

The broader mathematical context for the proposed projects is the theory of total positivity. Classically, a matrix is totally positive if all minors are positive. Lusztig extended the notion of total positivity to partial flag varieties, while Postnikov independently defined the positive Grassmannian. The combinatorics of total positivity is incredibly rich, leading to the definition of cluster algebras by Fomin and Zelevinsky. The PI proposes to study two generalizations of total positivity through a combinatorial lens. The first project concerns amplituhedra, which generalize the positive Grassmannian and arise in particle physics. The PI will work to resolve conjectures on the relationship between tilings of m=4 amplituhedra and the computation of scattering amplitudes, as well as various conjectures on tilings of m=2 amplituhedra. The second project concerns cluster structures on braid varieties, which generalize positive partial flag varieties. The PI will further develop the combinatorics of this cluster structure, investigating 3D plabic graphs and their relationship to weaves, and explore applications.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349015","Combinatorics of Total Positivity: Amplituhedra and Braid Varieties","DMS","Combinatorics","09/01/2024","03/25/2024","Melissa Sherman-Bennett","MA","Massachusetts Institute of Technology","Standard Grant","Stefaan De Winter","09/30/2024","$180,000.00","","msherben@mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","797000","","$0.00","The answers to real world problems, such as determining the behavior of particles in particle accelerators, are often quite complicated. Mathematics abstracts these complicated behaviors, and often reveals hidden structures; abstraction allows one to see the forest rather than the trees. For example, physicists Arkhani-Hamed and Trnka uncovered a high-dimensional mathematical object called the ""amplituhedron"" whose geometry should govern particle scattering. However, as abstraction increases, intuition decreases; it is easy to lose sight of the trees among the clouds. Algebraic combinatorics, as a mathematical discipline, is a tool to represent abstract mathematics in a more concrete way--similar to how a bar graph or scatter plot is a tool to represent a long list of numbers in a more intuitive way. In the case of the amplituhedron, combinatorics provides a way to break the amplituhedron up into smaller, simpler pieces. It also provides a way to visualize each piece, even though the pieces do not fit in three dimensions. It is through this combinatorics that the conjectural relationship between the amplituhedron and particle scattering is most apparent. In one project the PI will work to prove this conjectural relationship with collaborators Even-Zohar, Lakrec, Parisi, Tessler, and Williams. In general, the PI will seek to better understand the combinatorics of amplituhedra and related mathematical objects called cluster varieties. The PI will involve both undergraduate and graduate students in thisd research.

The broader mathematical context for the proposed projects is the theory of total positivity. Classically, a matrix is totally positive if all minors are positive. Lusztig extended the notion of total positivity to partial flag varieties, while Postnikov independently defined the positive Grassmannian. The combinatorics of total positivity is incredibly rich, leading to the definition of cluster algebras by Fomin and Zelevinsky. The PI proposes to study two generalizations of total positivity through a combinatorial lens. The first project concerns amplituhedra, which generalize the positive Grassmannian and arise in particle physics. The PI will work to resolve conjectures on the relationship between tilings of m=4 amplituhedra and the computation of scattering amplitudes, as well as various conjectures on tilings of m=2 amplituhedra. The second project concerns cluster structures on braid varieties, which generalize positive partial flag varieties. The PI will further develop the combinatorics of this cluster structure, investigating 3D plabic graphs and their relationship to weaves, and explore applications.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2408008","A graphon-based approach to seriation and an application in GSP","DMS","OFFICE OF MULTIDISCIPLINARY AC, Combinatorics","08/15/2024","08/09/2024","Mahya Ghandehari","DE","University of Delaware","Standard Grant","Tomek Bartoszynski","07/31/2027","$238,061.00","","mahya@udel.edu","220 HULLIHEN HALL","NEWARK","DE","197160099","3028312136","MPS","125300, 797000","9150","$0.00","This is an age of data, much of which is in the form of large networks, such as social networks, biological networks, or neural cell networks. These real-life networks are very complex, and understanding their structure is crucial for developing robust and efficient algorithms on them. The Principal Investigator (PI) aims to develop a systematic mathematical approach for analyzing and visualizing large networks. By integrating two different areas of mathematics, namely Discrete Mathematics and Analysis, the PI plans to extract large-scale features of networks using mathematical limit theories. Potential practical applications of this research include diverse instances such as data analysis in sociology, psychology, and image processing. Additionally, the PI is dedicated to teaching and training graduate and undergraduate students. To support this, the PI will supervise student research on problems related to this topic. Moreover, the PI will organize two events at the University of Delaware: one for high school students and another for undergraduate students.

A fundamental problem in the analysis of networks is to uncover their ?hidden spatial layout?, i.e. to label their vertices according to the spatial features of the network. This is the well-known seriation problem, a challenging problem in machine learning. In recent years, various heuristics and algorithms for the approximate versions of the seriation problem have been developed, but there is little theoretical evidence for why these methods should perform successfully or how they can be extended to the multi-dimensional case. Here, we discuss several intriguing and challenging questions regarding robustness/consistency of spectral seriation and its generalizations to higher dimensions. Graphons offer a non-parametric approach to network modeling, that is highly valuable when studying stochastic networks. Employing the powerful theory of dense/sparse graph limits, the PI plans to answer questions about stochastic networks (large discrete structures that vary over time) by inspecting the associated graphons (fundamental limit). To address the multi-dimensional case, the PI will develop a novel robust parameter which measures the extent of n-dim spatiality of a network. The PI will then investigate how spatial graphons can be used to provide instance-independent graph signal processing methods for real-life networks. Moreover, the results of this research will lead to further interactions between graphon theory, functional analysis, and learning theory.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348501","Algebraic Combinatorics","DMS","Combinatorics","08/15/2024","08/07/2024","Sergey Fomin","MI","Regents of the University of Michigan - Ann Arbor","Continuing Grant","Stefaan De Winter","07/31/2028","$100,000.00","","fomin@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","797000","","$0.00","Combinatorics studies discrete structures such as finite sets, graphs, and permutations. Many continuous phenomena allow for discrete representation, lending themselves amenable to combinatorial approaches. In algebraic combinatorics, it is often the case that similar combinatorial structures turn out to underlie seemingly unrelated mathematical phenomena. As a result, hidden connections are revealed, allowing the transfer of insights and techniques from one discipline to another. This project aims to extend and deepen such connections. It investigates combinatorial structures arising in algebra and geometry and is motivated by several classical areas of mathematics. On the geometric side, it aims to develop new combinatorial techniques in classical incidence geometry. This is a classical subject that has its roots in antiquity. It studies configurations of geometric objects, such as points, curves, and surfaces, focusing exclusively on their relative position. The algebraic side of the project concerns further development of the theory and applications of cluster algebras and their underlying combinatorial structures that have found applications in many areas of mathematics and theoretical physics. The project will involve students at various levels.

Incidence geometry is famous for a panoply of beautiful theorems discovered over the course of centuries. A recently proposed combinatorial approach utilizes tilings of oriented surfaces to place all these results under one roof. This approach has already been used to discover new incidence theorems and to generalize several known ones. It suggests multiple directions of further research, including those involving non-Euclidean geometries and/or varieties of higher degree, as well as new connections with discrete integrable systems and low-dimensional topology. Another part of the project is dedicated to further development of the theory of cluster algebras. These algebras, and the underlying combinatorics of quiver mutations, have found applications in many mathematical disciplines including representation theory, Teichmüller theory, mathematical physics, and symplectic geometry. One research direction concerns the structural theory of cluster algebras, more specifically the study of quiver mutations and associated invariants. Another direction aims to deepen our understanding of real plane algebraic curves and related concepts of singularity theory and low-dimensional topology, by revealing and investigating associated cluster-algebraic structures.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -9,18 +12,18 @@ "2349063","Extremal Point Configurations","DMS","Combinatorics","08/15/2024","08/06/2024","Alexey Glazyrin","TX","The University of Texas Rio Grande Valley","Continuing Grant","Stefaan De Winter","07/31/2027","$58,534.00","","Alexey.Glazyrin@utrgv.edu","1201 W UNIVERSITY DR","EDINBURG","TX","785392909","9566652889","MPS","797000","","$0.00","This project is devoted to the study of extremal point configurations, both in continuous cases such as Euclidean spaces or spheres and in discrete spaces. One particular area of focus is packing problems. A typical question in this area is to find the most efficient, or dense, packing. These types of questions have been well known in mathematics and science for a long time, starting with the Kepler conjecture about the densest sphere packing in three dimensions and with the kissing number problem that was the subject of disagreement between Isaac Newton and David Gregory at the end of the 17th century. A second focus area is the search for configurations that minimize energy. Probably the most famous example of this type is the Thomson problem asking to find the location of electrons in the sphere with the smallest cumulative electrostatic energy. The PI plans to mentor both undergraduate and graduate students and reach out to a wider audience by organizing research talks and public lectures.

In more detail, this project will focus on the study and applications of extremal point configurations. One direction of research concerns sets with few pairwise distances. In the discrete case, sets with few distances are the subject of the Erd?s?Ko?Rado and similar theorems. In the continuous case, one of the important objects of study is the set of equiangular lines. The PI will apply and extend the general method of finding upper bounds on sets with prescribed distances in two-point homogeneous spaces, including both the discrete and continuous regimes. A second direction of research concerns plank covering problems, that is, coverings of convex regions in Euclidean space by the regions between pairs of parallel hyperplanes. These questions go back to the Tarski problem and the Fejes Tóth zone conjecture. Recently, a version of the polynomial method brought several far-reaching generalizations of the results in this area. The PI will further develop this method and apply it to plank coverings and similar problems. Finally, a third direction of research is the study of energetically optimal configurations using a variety of analytic and optimization methods, including linear programming and semi-definite programming approach, with the goal of solving relevant problems in discrete and convex geometry.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348909","Cluster Algebras, Combinatorics and Knot Theory","DMS","Combinatorics","08/01/2024","08/01/2024","Ralf Schiffler","CT","University of Connecticut","Continuing Grant","Stefaan De Winter","07/31/2027","$194,385.00","","schiffler@math.uconn.edu","438 WHITNEY RD EXTENSION UNIT 11","STORRS","CT","062699018","8604863622","MPS","797000","","$0.00","The theory of cluster algebras is a highly active research area in mathematics that was initiated in 2002. The original motivation came from representation theory, a branch of modern algebra which is concerned with studying the symmetries of an algebraic structure rather than studying the structure itself. Representation theory has numerous applications in physics and chemistry as well as in other mathematical fields. Cluster algebras capture fundamental underlying combinatorial patterns that occur throughout representation theory. Quite remarkably, these patterns turn out to be present as well in a number of other branches of mathematics and physics that had previously seemed mostly unrelated. This project will contribute to the development of cluster algebras and their relations to other areas, in particular to knot theory and representations of algebras. The project will involve graduate students in the proposed research.

The project has several objectives. The principal investigator will develop a fundamental connection between cluster algebras and knot theory that realizes important knot invariants as specializations of cluster variables. The centerpiece of this project is the construction of a cluster algebra from an arbitrary knot or link, such that the cluster algebra contains a cluster in which each cluster variable specializes to the Alexander polynomial of the knot. The second objective is to study Cohen-Macaulay modules over 2-Calabi-Yau tilted algebras. These are non-commutative algebras that are associated to the clusters of a cluster algebra via categorification. One overarching goal is the classification of 2-Calabi-Yau tilted algebras that admit only finitely many Cohen-Macaulay modules. A third aim is to study maximal almost rigid modules, a new concept in representation theory inspired by the PI?s previous work on Catalan combinatorics. In this project, he PI will show that the triangulations of a surface with marked points and dissection correspond bijectively to the maximal almost rigid modules over an algebra associated to the surface dissection.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2428573","Conference: ALGECOM (Algebra, Geometry, and Combinatorics) Conference Series","DMS","Combinatorics","09/01/2024","07/31/2024","Alexander Yong","IL","University of Illinois at Urbana-Champaign","Continuing Grant","Stefaan De Winter","08/31/2027","$16,400.00","Peter Tingley, David Speyer","ayong@uiuc.edu","506 S WRIGHT ST","URBANA","IL","618013620","2173332187","MPS","797000","7556","$0.00","ALGECOM (algebra-geometry-combinatorics) is a series of biannual one day conferences. The central goal is to promote collaboration and regular interaction among Midwest students and faculty. Both (non-local) senior and early career mathematicians will be invited as speakers. ALGECOM is now a tradition in the Midwest going back to 2009. It has involved over fifty institutions. This grant will fund participant travel to six conferences, the first of which, ALGECOM XXIV is planned to be at the University of Minnesota, Twin Cities. A subsequent edition will occur at The Ohio State University. Both of these venues are new to the series. The conference website is at https://sites.google.com/view/algecom-main/algecom-main.

Each session of ALGECOM consists of four talks as well as a student poster session. Dissemination of research at the border of algebra, geometry and combinatorics is the main intellectual merit of the series. There is a wealth of Midwest departments with individually small ALGECOM-related research groups. These one-day conferences provide the stimulus for research collaboration among these groups. An effort has been made to encourage the attendance of graduate students, recent graduates, and untenured faculty. In terms of broader impacts, there are ongoing efforts to recruit members of underrepresented groups in mathematics as participants and speakers. These efforts are enhanced by NSF support, as it allows for invitations to mathematicians from a geographically larger region.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2348578","Polyhedral Challenges and Tools throughout Combinatorics","DMS","Combinatorics","08/01/2024","07/31/2024","Jesus De Loera","CA","University of California-Davis","Continuing Grant","Stefaan De Winter","07/31/2028","$137,324.00","","deloera@math.ucdavis.edu","1850 RESEARCH PARK DR STE 300","DAVIS","CA","956186153","5307547700","MPS","797000","","$0.00","The focus of this project is polytopes and polyhedra. These are jewel-like geometric structures that, because of their essential basic nature, have universal importance in many areas of pure and applied mathematics. For example, the scheduling of airplane crews and routing of airplanes requires fast computation with polytopes. Similarly, polytopes are enjoyed by school age children and teachers and have played a role in architecture, art, and philosophy for thousands of years. Despite their importance we still do not know the answer to some of the most basic mathematical questions about them. The PI plans to advance our mathematical understanding of polytopes. The PI's mathematical results and software will be directly relevant to a wide range of mathematicians but also to researchers in theoretical computer science. The PI will also continue his efforts in developing educational materials and software for training mathematicians in the use of polytopes. In fact, training of a new generation of computational mathematicians is key to his plans.

The PI will attack various problems about polytopes and develop useful tools for other researchers: in enumerative and extremal combinatorics the PI and his team will look at slices and shadows of polytopes, in algebraic combinatorics he will look at lattice points and a new (weighted, colored) Ehrhart theory, and in geometric-topological combinatorics the PI and his team will look at Baues complexes and related geometric constructions of fiber polytopes, floating bodies, illumination bodies, and others. Methods used by the PI include combinatorics, discrete mathematics, algebraic geometry, convex geometry, commutative algebra, lattices, representation theory, probability, and computer-aided experimentation, search, certification, and proofs. The PI will stress the emerging connection between Artificial Intelligence and polyhedral research.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2425253","Conference: Discrete integrable systems: difference equations, cluster algebras and probabilistic models","DMS","PROBABILITY, ALGEBRA,NUMBER THEORY,AND COM, Combinatorics","08/15/2024","08/01/2024","Rinat Kedem","IL","University of Illinois at Urbana-Champaign","Standard Grant","James Matthew Douglass","01/31/2025","$19,989.00","","rinat@illinois.edu","506 S WRIGHT ST","URBANA","IL","618013620","2173332187","MPS","126300, 126400, 797000","7556","$0.00","This grant supports travel for US participants in the program ""Discrete integrable systems: difference equations, cluster algebras and probabilistic models,"" that will take place October 20 to November 1, 2024 at the International Center for Theoretical Sciences in Bangalore, India. The program includes a one-week introductory school, including three lecture series by experts in cluster algebras, integrability and probability, directed at graduate students and early career mathematicians. This will be followed by a one-week conference that will include presentations by senior researchers in the field. The grant will support the travel of early career mathematicians from the US to the conference, where they will interact and form research collaborations with researchers and leading experts from around the world.

The program focuses on three interrelated aspects of discrete integrability at the interface of mathematics and theoretical physics, which have seen intense research activity of late: (1) The study of singularities of integrable difference equations and ultra-discretization of these equations, such as box-ball systems. (2) The interplay between discrete integrable systems and cluster algebras, with applications to discrete geometry and statistical mechanics. (3) Applications to integrable probability, solvable vertex models and the theory of symmetric functions. The program webpage is https://www.icts.res.in/program/DISDECAP2024.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349024","Random Processes and Constrained Combinatorial Structures","DMS","Combinatorics","08/01/2024","08/01/2024","Menahem Simkin","MA","Massachusetts Institute of Technology","Standard Grant","Stefaan De Winter","07/31/2027","$162,172.00","","msimkin@mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","797000","","$0.00","This project aims to use randomized algorithms to address the fundamental combinatorial problem of constructing interesting objects, counting such objects, and studying their (typical) structure. Beginning in the mid-twentieth century, the use of randomness and the probabilistic method revolutionized the combinatorialist's toolbox. More recently, the application of randomized processes has facilitated many breakthroughs and landmark results. The study and use of these processes has deep connections to functional analysis, entropy theory, and discrete probability. By nature, the use of these processes also opens the door to computer experimentation. As such, many aspects of this project are suitable for collaboration with students of all levels.

One focus of the project is the study of graphs and hypergraphs where, in the standard random models, different constraints compete at the same scale. For instance, consider Latin squares, that is, n x n matrices in which every row and column is a permutation of the symbols {1,2,...,n}. It is straightforward to verify that if one chooses each symbol independently and uniformly at random then in each row and column, a constant fraction of the symbols will be repeated. For this reason (and others), probabilistic constructions of Latin squares proved challenging. Nevertheless, recent advances allowed the use of sophisticated randomized algorithms in constructing Latin squares, which are but one example of the rich family of combinatorial designs. Despite this progress, many mysteries remain regarding even the most basic properties of random Latin squares (and related objects). For example, how many 2x2 Latin subsquares does a typical random order-n Latin square have? A second focus of the project is the study of threshold phenomena in random hypergraphs. Of particular interest is characterizing at which densities random binomial graphs contain certain spanning structures, such as combinatorial designs. A recently proved connection between ""fractional expectation-thresholds"" and thresholds introduces an exciting avenue for using randomized constructions to prove threshold results. This project will develop and extend techniques based on randomized processes to answer these constructive, enumerative, and structural questions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348859","Connections in Extremal Combinatorics","DMS","Combinatorics","08/01/2024","07/31/2024","David Conlon","CA","California Institute of Technology","Continuing Grant","Stefaan De Winter","07/31/2027","$10,000.00","","dconlon@caltech.edu","1200 E CALIFORNIA BLVD","PASADENA","CA","911250001","6263956219","MPS","797000","","$0.00","Extremal combinatorics is that part of discrete mathematics that studies how large or small a collection of finite objects can be under given restrictions and has broad connections with number theory, discrete geometry, probability, theoretical computer science and beyond. Recent advances in this area have brought to the fore several unexpected connections between seemingly disparate problems. In this project, the PI will explore some of these connections further to resolve several old problems in the area and forge further connections with other areas. The research will involve graduate students and postdocs.

Of particular interest are the recent breakthroughs in graph Ramsey theory and the advance of Mattheus and Verstraëte specifically, which has revealed intriguing connections between the study of off-diagonal Ramsey numbers and problems in extremal graph theory and finite geometry. The PI also intend to build on previous progress by the PI and his collaborators to make further progress in graph Ramsey theory, extremal graph theory and the fundamental areas of additive combinatorics and discrete geometry. In doing so, the PI expects to open further connections and increase interactions between extremal combinatorics and important recent trends in the study of high-dimensional expansion, convex geometry and algebraic combinatorics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2348578","Polyhedral Challenges and Tools throughout Combinatorics","DMS","Combinatorics","08/01/2024","07/31/2024","Jesus De Loera","CA","University of California-Davis","Continuing Grant","Stefaan De Winter","07/31/2028","$137,324.00","","deloera@math.ucdavis.edu","1850 RESEARCH PARK DR STE 300","DAVIS","CA","956186153","5307547700","MPS","797000","","$0.00","The focus of this project is polytopes and polyhedra. These are jewel-like geometric structures that, because of their essential basic nature, have universal importance in many areas of pure and applied mathematics. For example, the scheduling of airplane crews and routing of airplanes requires fast computation with polytopes. Similarly, polytopes are enjoyed by school age children and teachers and have played a role in architecture, art, and philosophy for thousands of years. Despite their importance we still do not know the answer to some of the most basic mathematical questions about them. The PI plans to advance our mathematical understanding of polytopes. The PI's mathematical results and software will be directly relevant to a wide range of mathematicians but also to researchers in theoretical computer science. The PI will also continue his efforts in developing educational materials and software for training mathematicians in the use of polytopes. In fact, training of a new generation of computational mathematicians is key to his plans.

The PI will attack various problems about polytopes and develop useful tools for other researchers: in enumerative and extremal combinatorics the PI and his team will look at slices and shadows of polytopes, in algebraic combinatorics he will look at lattice points and a new (weighted, colored) Ehrhart theory, and in geometric-topological combinatorics the PI and his team will look at Baues complexes and related geometric constructions of fiber polytopes, floating bodies, illumination bodies, and others. Methods used by the PI include combinatorics, discrete mathematics, algebraic geometry, convex geometry, commutative algebra, lattices, representation theory, probability, and computer-aided experimentation, search, certification, and proofs. The PI will stress the emerging connection between Artificial Intelligence and polyhedral research.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2341774","Random Structures and Algorithms","DMS","Combinatorics","08/01/2024","07/31/2024","ALAN FRIEZE","PA","Carnegie-Mellon University","Standard Grant","Stefaan De Winter","07/31/2027","$270,000.00","","af1p@andrew.cmu.edu","5000 FORBES AVE","PITTSBURGH","PA","152133815","4122688746","MPS","797000","","$0.00","In this project the PI will study various properties of random graphs/networks. Such objects arise frequently in economics, such as transport networks, as models of social media platforms and even as the relations between proteins in animal cells. These networks are highly complex and are best modelled as if they have been randomly constructed. Typically, there are computational problems associated with such structures. For example in routing trucks one is faced with the problem of finding routes that minimize some objective. The PI will study such problems within a stochastic framework. Graduate students and postdocs will be involved in the project.

The PI will study the typical structure of combinatorial objects. He will study random graphs and hypergraphs and determine thresholds for the existence of various properties. There are still many unanswered questions about Matchings, Hamilton cycles and Spanning Trees in this context and the PI will seek to answer some of them. This will involve questions where the edges have weights and colors. The PI will also consider the algorithmic questions that arise if one wants to find algorithms that work well in the average case. In some sense, this is an attempt to explain why NP-completeness is not necessarily a barrier to obtaining results in practice. In particular, the PI will study the expected performance of branch and bound algorithms, one of the most successful general approaches to hard problems. Finally, he will study combinatorial games that arise: usually Maker-Breaker games where Breaker tries to foil Maker's attempts at achieving some objective.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2417981","Conference: New Trends in Geometry, Combinatorics and Mathematical Physics","DMS","ALGEBRA,NUMBER THEORY,AND COM, Combinatorics","08/01/2024","07/26/2024","Natalia Rojkovskaia","KS","Kansas State University","Standard Grant","James Matthew Douglass","07/31/2025","$17,500.00","","rozhkovs@math.ksu.edu","1601 VATTIER STREET","MANHATTAN","KS","665062504","7855326804","MPS","126400, 797000","7556, 9150","$0.00","The project supports travel of the US-based mathematicians to the international conference New Trends in Geometry, Combinatorics and Mathematical Physics, that will be take place October 21-25, 2024 at the CNRS center la Vieille Perrotine - Oleron, France. The goal of the project is to provide opportunities for early-career, US-based researchers and to boost the visibility and impact of US-based research. Early-career participants will benefit by acquiring new scientific knowledge from international experts and building long-term professional connections. Ultimately, participation of US-based researchers in the conference will have a positive impact on research projects conducted in the United States.

The scientific foci of the conference are differential geometry and algebraic combinatorics, with applications to mathematical physics. More specifically, applications of cluster algebras in integrable systems and mathematical physics. These applications will be a main topic of the conference, along with interactions between cluster algebras and complex geometry. Further applications of cluster algebras in physics will also be highlighted. Participants from a wide variety of backgrounds will serve to boost the exchange of methods, applications and new ideas, and will form foundations for continuing collaborations. This project is jointly funded by the Algebra and Number Theory and the Combinatorics programs. The conference website is https://indico.math.cnrs.fr/event/11259/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413439","Conference: The 9th International Symposium on Riordan Arrays and Related Topics","DMS","Combinatorics","06/01/2024","05/21/2024","Dennis Davenport","DC","Howard University","Standard Grant","Stefaan De Winter","05/31/2025","$15,000.00","Louis Shapiro","dennis.davenport@howard.edu","2400 6TH ST NW","WASHINGTON","DC","200590002","2028064759","MPS","797000","7556","$0.00","This award supports participation in the 9th International Symposium on Riordan Arrays and Related Topics (9RART), scheduled to occur at Howard University in Washington, D.C. from June 3rd to June 5th. Notably, there is a significant historical tie to this event, as the original paper on the Riordan group was authored by four mathematicians from Howard University in 1991. Since then, eight international conferences have taken place, but this is the first to be held at Howard University. The primary objective of the symposium is to foster collaboration and networking among researchers interested in Riordan arrays and associated subjects. It seeks to catalyze fresh research directions, offer platforms for emerging scholars to showcase their work, and serve as an international nexus for academic exchange and cooperation. Additionally, it aims to broaden the community of mathematicians engaged in Riordan array research.

The symposium features two distinguished international scholars specializing in enumerative combinatorics, who deliver hour-long colloquium-style lectures on their respective fields of expertise. These lectures provide comprehensive overviews of current research trends and suggest potential avenues for future exploration. Furthermore, the event hosts four keynote speakers recognized for their contributions to Riordan arrays. Additionally, there are scheduled several 30-minute presentations and a poster session showcasing student research. The conference website is : https://riordanarray.org/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2400268","Conference: CombinaTexas 2024-2026","DMS","Combinatorics","03/01/2024","02/23/2024","Chun-Hung Liu","TX","Texas A&M University","Continuing Grant","Stefaan De Winter","02/28/2027","$13,320.00","Huafei Yan, Jacob White, Laura Matusevich","chliu@math.tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","797000","7556","$0.00","The CombinaTexas 2024 conference will be held at Texas A&M University, College Station, TX, on March 23-24, 2024. The conference will feature five fifty-minute plenary lectures and a number of contributed talks in various areas of Combinatorics and Graph Theory. The aim of the CombinaTexas series is to enhance communication among mathematicians in Texas and surrounding states, promote research activities of the local combinatorics community, and provide a platform for the presentation and discussion of the latest developments in the broad field of combinatorics. Ever since Texas A&M University hosted the first conference in 2000, it has been held almost every year at an institution in the South Central United States. CombinaTexas 2024 is the 20th conference in this series. The CombinaTexas conference series will be continuously held in 2025 and 2026 supported by this award.

The topics of the CombinaTexas Series include all branches of Combinatorics, Graph Theory, and their connections to Algebra, Geometry, Probability Theory, and Computer Science. In 2024 the confirmed plenary speakers are Boris Bukh (Carnegie Mellon University), Sam Hopkins (Howard University), Jeremy Martin (University of Kansas), Jessica Striker (North Dakota State University), and Fan Wei (Duke University). They will cover topics in Algebraic Combinatorics, Extremal Combinatorics, Discrete Geometry, Graph Theory and their interaction with Algebraic Geometry, Commutative Algebra, and Computer Science. About 70 participants are anticipated, with an estimated 20 contributed talks in parallel sessions. More information about the conference will be available at the webpage https://www.math.tamu.edu/conferences/combinatexas/""

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348843","Combinatorial Representation Theory of Quantum Groups and Coinvariant Algebras","DMS","Combinatorics","07/01/2024","03/25/2024","Joshua Swanson","CA","University of Southern California","Standard Grant","Stefaan De Winter","06/30/2027","$180,000.00","","swansonj@usc.edu","3720 S FLOWER ST FL 3","LOS ANGELES","CA","90033","2137407762","MPS","797000","","$0.00","Combinatorics has been described as the nanotechnology of mathematics. It is concerned with counting discrete objects, which naturally arise in many applications. As one example, software development frequently requires choosing between different algorithms to solve a problem. Combinatorics allows one to count the number of steps each candidate algorithm takes and then choose the best solution. In this way, combinatorics provides a set of basic tools and a collection of argument prototypes that guide the solution of problems throughout STEM. One of the virtues of combinatorics research is that it provides students with concrete opportunities to develop problem-solving, software development, and other key skills.

Algebraic combinatorics, more specifically, focuses on the combinatorial essence of highly structured and often advanced problems coming from topology, representation theory, particle physics, and other areas. Such problems are frequently reduced in some fashion to an intricate combinatorial analysis. One such algebraic problem is to understand quantum groups. These remarkable structures arose around 1980 from connections with integrable lattice models in quantum mechanics, and some of the technically deepest theories in pure mathematics and physics are in this area. One of the main focuses of the present project is to further develop certain combinatorial diagrams called web bases. These combinatorial objects encode the representation category of quantum groups and allow for efficient computations with powerful topological quantum invariants. They connect a remarkably diverse collection of topics, including total positivity, alternating sign matrices, plane partitions, crystal bases, dynamical algebraic combinatorics, and the geometry of the affine Grassmannian. Students will be involved in the research project.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2429145","Conference: Binghamton University Graduate Combinatorics, Algebra, and Topology Conference (BUGCAT Conference) 2024,2025,2026","DMS","ALGEBRA,NUMBER THEORY,AND COM, Combinatorics","09/15/2024","07/16/2024","Alexander Borisov","NY","SUNY at Binghamton","Continuing Grant","Andrew Pollington","08/31/2027","$28,000.00","","borisov@math.binghamton.edu","4400 VESTAL PKWY E","BINGHAMTON","NY","139024400","6077776136","MPS","126400, 797000","7556","$0.00","This award supports the BUGCAT Conference (Binghamton University Graduate Combinatorics, Algebra, and Topology Conference) 2024 which will take place at the Binghamton University campus on October 26-27, 2024 and also tosupport the conference in the fall of 2025 and 2026. This conference has been running since 2008, with support from NSF in many years, including the last three in-person conferences, in 2019, 2022, and 2023. Continuing NSF support will allow to keep the conference at a current level of more than 100 registered participants, three hour-long keynote presentations, and 40-45 contributed talks of 20-25 minutes in length. The three keynote speakers are professional mathematicians, while most of the other participants are graduate students, with some postdocs and undergraduates.

The conference is run by a rotating committee of graduate students, with general oversight and guidance from the P.I. and some other faculty members. This helps to maintain a friendly and inclusive atmosphere, to facilitate free scientific interactions at the level appropriate for the beginning researchers at various stages of their mathematical development. This also gives the graduate student organizers experience in running a larger conference, and helps them appreciate what is involved in this, when they go give talks at conferences elsewhere. The organizers make efforts to encourage diversity, both by virtue of the varied backgrounds of the organizing committee members, and by the selection of the keynote speakers, without sacrificing the scientific level of the conference. The permanent conference website with the 2023 information, and some previous years' documents, can be found here: https://seminars.math.binghamton.edu/BUGCAT/index.html

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2409861","Conference: An Undergraduate Research Program in Combinatorics","DMS","Combinatorics","06/15/2024","06/03/2024","Joseph Gallian","MN","University of Minnesota Duluth","Continuing Grant","Stefaan De Winter","05/31/2026","$49,109.00","","jgallian@d.umn.edu","1035 UNIVERSITY DR # 133","DULUTH","MN","558123031","2187267582","MPS","797000","7556","$0.00","This award partially supports two meetings of the Undergraduate Research Program in Combinatorics at the University of Minnesota Duluth. The first meeting will be held June 9 - August 1, 2024. In particular, the award supports two graduate assistants at the summer undergraduate research program during the 2024 and 2025 summer. These graduate assistants will assist the PI and co-director of the program. The graduate assistants will be engaged in all aspects of the program: finding suitable problems, acting as mentors and role models, interacting mathematically and socially with participants and visitors, holding practice sessions for presentations, arranging social activities, reading manuscripts, providing advice about graduate schools and fellowships, writing evaluations of the participants' research that the directors of the program use for letters of recommendation. They will likely continue their mentorship activities after the program is over: such as being a coauthor with participants on papers written after the summer program.


The Undergraduate Research Program in Combinatorics will contribute to the advancement of combinatorics by resolving conjectures and answering questions in the literature of interest to well-established people in the field. New methods and concepts and novel applications and examples will be introduced. Some papers will provide deeper insights and better ways to think about concepts. The most significant impact the Duluth programs in 2024 and 2025 will have is the training of future generations of mathematicians who will foster undergraduate and graduate research when they become professionals.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2404924","Conference: Summer School on Cluster Algebras and Related Topics","DMS","Combinatorics","06/15/2024","06/03/2024","Ralf Schiffler","CT","University of Connecticut","Standard Grant","Stefaan De Winter","11/30/2025","$47,996.00","Emily Gunawan","schiffler@math.uconn.edu","438 WHITNEY RD EXTENSION UNIT 11","STORRS","CT","062699018","8604863622","MPS","797000","7556","$0.00","The Cluster Algebra Summer School takes place at the University of Connecticut June 17-21, 2024. It is aimed at graduate and advanced undergraduate students, and it comprises four mini-courses on different recent developments in the theory of cluster algebras and related topics. This theory is a relatively young branch of mathematics. The initial motivation was to gain an understanding of certain positivity properties in representation theory, a branch of modern algebra. The theory quickly developed deep connections to a variety of disciplines in mathematics and physics, and it is a highly active research area. Cluster algebras are commutative rings equipped with a combinatorial structure that groups its elements into certain subsets, called clusters, which are related to each other via an intricate apparatus called mutation. This structure turns out to be very natural, in the sense that it is present in a large number of mathematical designs.

The four mini-courses are on the following topics. (1) Cluster structures on Richardson varieties and their categorification, which focuses on a relation between representation theory and cluster algebras in the setting of algebras arising from Grassmannian varieties. (2) Cluster algebras and Legendrian links, a mini-course on a connection between cluster algebras and symplectic geometry, especially the contact structure on positive braids. (3) Maximal almost rigid modules, a new type of modules over gentle algebras that correspond bijectively to triangulations of surfaces. (4) Cluster algebras and knot theory, which is on a fundamental relation to knots and links that gives new insights into both areas. All courses are on recent advances in the field and are taught by researchers who are directly involved in these developments. This summer school will help to prepare a diverse group of junior mathematicians to work in this important field. The url for the website of the school is https://egunawan.github.io/cass24/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2409861","Conference: An Undergraduate Research Program in Combinatorics","DMS","Combinatorics","06/15/2024","06/03/2024","Joseph Gallian","MN","University of Minnesota Duluth","Continuing Grant","Stefaan De Winter","05/31/2026","$49,109.00","","jgallian@d.umn.edu","1035 UNIVERSITY DR # 133","DULUTH","MN","558123031","2187267582","MPS","797000","7556","$0.00","This award partially supports two meetings of the Undergraduate Research Program in Combinatorics at the University of Minnesota Duluth. The first meeting will be held June 9 - August 1, 2024. In particular, the award supports two graduate assistants at the summer undergraduate research program during the 2024 and 2025 summer. These graduate assistants will assist the PI and co-director of the program. The graduate assistants will be engaged in all aspects of the program: finding suitable problems, acting as mentors and role models, interacting mathematically and socially with participants and visitors, holding practice sessions for presentations, arranging social activities, reading manuscripts, providing advice about graduate schools and fellowships, writing evaluations of the participants' research that the directors of the program use for letters of recommendation. They will likely continue their mentorship activities after the program is over: such as being a coauthor with participants on papers written after the summer program.


The Undergraduate Research Program in Combinatorics will contribute to the advancement of combinatorics by resolving conjectures and answering questions in the literature of interest to well-established people in the field. New methods and concepts and novel applications and examples will be introduced. Some papers will provide deeper insights and better ways to think about concepts. The most significant impact the Duluth programs in 2024 and 2025 will have is the training of future generations of mathematicians who will foster undergraduate and graduate research when they become professionals.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2344639","Conference: Conference on Enumerative and Algebraic Combinatorics","DMS","Combinatorics","02/15/2024","02/08/2024","Vincent Vatter","FL","University of Florida","Standard Grant","Stefaan De Winter","01/31/2025","$22,356.00","Andrew Vince, Miklos Bona, Zachary Hamaker","vatter@ufl.edu","1523 UNION RD RM 207","GAINESVILLE","FL","326111941","3523923516","MPS","797000","7556","$0.00","The Conference on Enumerative and Algebraic Combinatorics will take place at the University of Florida in Gainesville, Florida, February 25-27, 2024. The conference will feature 25 invited and contributed talks by leading researchers in the field as well as a poster session. By bringing together those working in both the Enumerative and Algebraic Combinatorics communities, attending researchers will have ample opportunity to learn about recent developments and develop new mathematics.

The aims of the conference are to present outstanding recent developments in both enumerative and algebraic combinatorics, with a particular focus on their overlap. Specific topics will include standard Young tableaux, permutations, partially ordered sets, symmetric functions, lattice paths, and compositions, all of which are amenable to both enumerative and algebraic study. For more information see the conference web page: https://combinatorics.math.ufl.edu/conferences/sagan2024/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348799","Positive Geometry","DMS","Combinatorics","06/01/2024","05/22/2024","Thomas Lam","MI","Regents of the University of Michigan - Ann Arbor","Continuing Grant","Stefaan De Winter","05/31/2027","$215,974.00","","tfylam@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","797000","","$0.00","The aim of this project is to develop ""positive geometry"". Positive geometry was first conceived of in the study of fundamental questions in particle physics: the calculation of scattering amplitudes that determine how elementary particles, such as electrons and photons, interact. Positive geometries are shapes (for example, higher dimensional versions of cubes and pyramids) whose structure reflects the behavior of particle interaction. In this project, the PI will develop the mathematical foundations of positive geometry which will in turn be applied to physical questions. The project will involve both undergraduate and graduate students.

Positive geometries are semi-algebraic spaces equipped with a differential form, the ""canonical form"", whose polar structure reflects the facial structure of the geometry. Examples of positive geometries include convex polytopes, positive parts of toric varieties, totally nonnegative flag varieties, and conjecturally Grassmann polytopes and amplituhedra. This project aims to study the combinatorics, topology, and geometry of positive geometries in analogy with the theory of convex polytopes. The project will find new positive geometries and new formulae for canonical forms, and apply this to the theory of scattering amplitudes in physics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2408960","Conference: A Celebration of Algebraic Combinatorics","DMS","Combinatorics","06/01/2024","05/14/2024","Lauren Williams","MA","Harvard University","Standard Grant","Stefaan De Winter","11/30/2025","$49,500.00","","williams@math.harvard.edu","1033 MASSACHUSETTS AVE STE 3","CAMBRIDGE","MA","021385366","6174955501","MPS","797000","7556","$0.00","The conference ``A celebration of algebraic combinatorics'' takes place on June 3-7, 2024, at the Harvard Geological lecture hall at Harvard University. It covers many aspects of combinatorics, a field which was extensively developed by Richard Stanley through his work in algebraic, topological, geometric, and enumerative combinatorics. The conference presents a chance to bring together both experts in the field and early career mathematicians to learn about the latest developments in the field.

The talks at the conference cover a range of topics, ranging from total positivity, symmetric functions, Schubert calculus, poset topology, polytopes, to cluster algebras, log-concavity, the dimer model, and connections with probability. Besides the talks, there are plans to have an open problem session. The website for the conference can be found at https://www.math.harvard.edu/event/math-conference-honoring-richard-p-stanley/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." diff --git a/Computational-Mathematics/Awards-Computational-Mathematics-2024.csv b/Computational-Mathematics/Awards-Computational-Mathematics-2024.csv index 35d2693..72e6d6e 100644 --- a/Computational-Mathematics/Awards-Computational-Mathematics-2024.csv +++ b/Computational-Mathematics/Awards-Computational-Mathematics-2024.csv @@ -1,4 +1,6 @@ "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract" +"2422470","Collaborative Research: NSF-NSERC: Data-enabled Model Order Reduction for 2D Quantum Materials","DMS","COMPUTATIONAL MATHEMATICS, CONDENSED MATTER & MAT THEORY, CDS&E","09/01/2024","08/20/2024","Vikram Gavini","MI","Regents of the University of Michigan - Ann Arbor","Standard Grant","Jodi Mead","08/31/2027","$288,693.00","","vikramg@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","127100, 176500, 808400","054Z, 079Z, 095Z, 7569, 9216, 9263","$0.00","The project will provide state-of-the-art computational tools for the development of novel 2D materials and their potential application to ultra-fast electronic, opto-electronic, and magnetic devices; unconventional optical and photonic devices; communication devices; and quantum computing applications. The project will address interconnected challenges in emerging areas of quantum science, computational mathematics and computer science by effectively merging highly domain-specific techniques with general machine learning techniques, thus informing and motivating analogous research on model order reduction across the sciences and engineering. 2D materials research is an ideal platform to motivate new mathematics training and curricula in the analysis, modeling, and computation of electronic structure, mechanical and topological properties of materials, and analysis of experimental data. The project?s outreach to female and underrepresented student populations will broaden the diversity of the mathematical research community, and the project provides research training opportunities for graduate students.

Many quantum phenomena of scientific and technological interest emerge naturally at the moiré length scales of layered 2D materials which makes those materials an exciting platform to explore quantum materials properties and to prototype quantum devices. For example, correlated electronic phases such as superconductivity have been recently observed in twisted bilayer graphene (tBLG). Such pioneering results have opened up a new era in the investigation and exploitation of quantum phenomena. Despite the continuing increase in computational resources, high-fidelity modeling and simulation of many quantum materials systems remains out of reach. The limitation is particularly serious in 2D heterostructures due to the large scales at which the quantum phenomena of interest emerge. The objective of this NSF-NSERC Alliance project is to develop an advanced computational modeling workflow, merging state-of-the-art quantum modeling and machine-learning methods to enable rapid, automated, high-fidelity exploration of mechanical and electronic properties of 2D quantum materials. This award is jointly supported by the Division of Mathematical Sciences, the Division of Materials Research and the Office of Advanced Cyberinfrastructure.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2422469","Collaborative Research: NSF-NSERC: Data-enabled Model Order Reduction for 2D Quantum Materials","DMS","COMPUTATIONAL MATHEMATICS, CONDENSED MATTER & MAT THEORY, CDS&E","09/01/2024","08/20/2024","Mitchell Luskin","MN","University of Minnesota-Twin Cities","Standard Grant","Jodi Mead","08/31/2027","$555,373.00","","luskin@math.umn.edu","200 OAK ST SE","MINNEAPOLIS","MN","554552009","6126245599","MPS","127100, 176500, 808400","054Z, 079Z, 095Z, 7569, 9216, 9263","$0.00","The project will provide state-of-the-art computational tools for the development of novel 2D materials and their potential application to ultra-fast electronic, opto-electronic, and magnetic devices; unconventional optical and photonic devices; communication devices; and quantum computing applications. The project will address interconnected challenges in emerging areas of quantum science, computational mathematics and computer science by effectively merging highly domain-specific techniques with general machine learning techniques, thus informing and motivating analogous research on model order reduction across the sciences and engineering. 2D materials research is an ideal platform to motivate new mathematics training and curricula in the analysis, modeling, and computation of electronic structure, mechanical and topological properties of materials, and analysis of experimental data. The project?s outreach to female and underrepresented student populations will broaden the diversity of the mathematical research community, and the project provides research training opportunities for graduate students.

Many quantum phenomena of scientific and technological interest emerge naturally at the moiré length scales of layered 2D materials which makes those materials an exciting platform to explore quantum materials properties and to prototype quantum devices. For example, correlated electronic phases such as superconductivity have been recently observed in twisted bilayer graphene (tBLG). Such pioneering results have opened up a new era in the investigation and exploitation of quantum phenomena. Despite the continuing increase in computational resources, high-fidelity modeling and simulation of many quantum materials systems remains out of reach. The limitation is particularly serious in 2D heterostructures due to the large scales at which the quantum phenomena of interest emerge. The objective of this NSF-NSERC Alliance project is to develop an advanced computational modeling workflow, merging state-of-the-art quantum modeling and machine-learning methods to enable rapid, automated, high-fidelity exploration of mechanical and electronic properties of 2D quantum materials. This award is jointly supported by the Division of Mathematical Sciences, the Division of Materials Research and the Office of Advanced Cyberinfrastructure.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2436343","Collaborative Research: MATH-DT: Mathematical Foundations of AI-assisted Digital Twins for High Power Laser Science and Engineering","DMS","OFFICE OF MULTIDISCIPLINARY AC, COMPUTATIONAL MATHEMATICS","10/01/2024","08/09/2024","Andrea Bertozzi","CA","University of California-Los Angeles","Standard Grant","Troy D. Butler","09/30/2027","$569,051.00","Sergio Carbajo","bertozzi@math.ucla.edu","10889 WILSHIRE BLVD STE 700","LOS ANGELES","CA","900244200","3107940102","MPS","125300, 127100","075Z, 079Z, 9263","$0.00","Laser technology is one of the most transformative inventions of the modern era, which has become an indispensable tool for scientific research and technological innovation - revolutionizing the semiconductor industry, telecommunications, healthcare, and defense. However, current laser design and manufacturing approaches remain stagnant, stymieing further breakthroughs. Developing novel integrated systems of laser architectures, components, and techniques leveraging digital twins (DT) is imperative to expand frontiers in intensity, wavelength regime, and high average power. This project will fill this gap using state-of-the-art predictive and generative artificial intelligence (AI) coupled with physical principles and high-fidelity, close-loop, rapid feedback between digital models and physical systems. Graduate students and postdoctoral researchers will also be integrated within the research team as part of the training of the next generation of scientists required to advance the field.

This project will develop theoretical foundations for AI-assisted DTs to integrate scientific data, physical models, and machine learning for complex high-power laser science and engineering (HPLSE) to enable efficient design, failure and performance prediction, operational optimization, and emerging lasing conditions. Laser technologies are extremely complex to model because they rely on a cascaded set of mode-locked laser dynamics and a manifold of architectures and configurations of chirped pulse amplification, and nonlinear optical stages, such as parametric amplification. Their architectural complexity and multi-dimensional data far exceed current modeling and analysis tools. The project will address these challenges by (1) extracting reduced representation of scientific data from experiments or high-fidelity HPLSE simulation, (2) building data-efficient and physics-aware predictive machine learning surrogate models of laser fields with uncertainty quantification, and (3) developing generative model-based rapid closed-loop control between digital models and physical high-power laser systems. The project will be AI-focused, multi-disciplinary, and involve a diverse workforce of future scientists and engineers. The project will also include an education thrust to integrate the research results into interdisciplinary education. The project will bolster AI foundations and its application curricula at both UCLA and the University of Utah. More critically, it will forge a robust collaboration among mathematics, data science, and laser technologies.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2436319","Collaborative Research: MATH-DT: Mathematical Foundations of Quantum Digital Twins","DMS","OFFICE OF MULTIDISCIPLINARY AC, COMPUTATIONAL MATHEMATICS","09/01/2024","08/09/2024","Daniel Appelo","VA","Virginia Polytechnic Institute and State University","Standard Grant","Jodi Mead","08/31/2027","$299,148.00","Xinwei Deng","appelo@vt.edu","300 TURNER ST NW","BLACKSBURG","VA","240603359","5402315281","MPS","125300, 127100","7203, 9263","$0.00","This project develops, analyzes, and deploys Quantum Digital Twins (QDTs), which are digital clones of existing quantum computers. Built within a comprehensive mathematical and statistical framework, these QDTs will enable bidirectional interactions between quantum computers and virtual models on classical systems, optimizing quantum performance and marking a significant step toward achieving the proverbial Quantum Leap in computational abilities. This advancement will help maintain the United States' leadership in quantum information science and technology, supporting the National Quantum Initiative Act and producing next-generation quantum-enabled technologies for sensing, information processing, communication, security, and computing. Additionally, the project establishes foundations that can enhance other Digital Twin technologies across various fields, from energy to health. It will also facilitate the interdisciplinary training of young scientists in modern data-driven computational methods and the experimental and theoretical aspects of quantum devices and digital twins, with outreach efforts to local communities and Native American tertiary colleges.

The QDTs developed in this project aim to overcome the limitations of traditional quantum simulations, which use a linear component-by-component approach, by introducing four key advancements: (i) the first-ever mathematical formulation of QDTs grounded in a Bayesian probabilistic framework, addressing the inherently probabilistic nature of quantum devices, (ii) new randomized Bayesian experimental design techniques tailored for QDTs, capable of handling the complex dynamics and uncertainties in quantum systems, (iii) a robust generalized Bayesian framework using optimal transportation theory with adaptive prior and model enrichment mechanisms, enabling QDTs to detect and correct their flaws while minimizing system downtime, and (iv) advanced risk-neutral techniques for quantum optimal control and validation, improving QDTs' ability to generate high-fidelity quantum gates. The project also integrates these algorithms and methods into existing open-source software products, demonstrating and disseminating the developed QDTs.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2436318","Collaborative Research: MATH-DT: Mathematical Foundations of Quantum Digital Twins","DMS","OFFICE OF MULTIDISCIPLINARY AC, COMPUTATIONAL MATHEMATICS","09/01/2024","08/09/2024","Mohammad Motamed","NM","University of New Mexico","Standard Grant","Jodi Mead","08/31/2027","$299,990.00","Gabriel Huerta","motamed@math.unm.edu","1700 LOMAS BLVD NE STE 2200","ALBUQUERQUE","NM","87131","5052774186","MPS","125300, 127100","7203, 7263, 9150, 9263","$0.00","This project develops, analyzes, and deploys Quantum Digital Twins (QDTs), which are digital clones of existing quantum computers. Built within a comprehensive mathematical and statistical framework, these QDTs will enable bidirectional interactions between quantum computers and virtual models on classical systems, optimizing quantum performance and marking a significant step toward achieving the proverbial Quantum Leap in computational abilities. This advancement will help maintain the United States' leadership in quantum information science and technology, supporting the National Quantum Initiative Act and producing next-generation quantum-enabled technologies for sensing, information processing, communication, security, and computing. Additionally, the project establishes foundations that can enhance other Digital Twin technologies across various fields, from energy to health. It will also facilitate the interdisciplinary training of young scientists in modern data-driven computational methods and the experimental and theoretical aspects of quantum devices and digital twins, with outreach efforts to local communities and Native American tertiary colleges.

The QDTs developed in this project aim to overcome the limitations of traditional quantum simulations, which use a linear component-by-component approach, by introducing four key advancements: (i) the first-ever mathematical formulation of QDTs grounded in a Bayesian probabilistic framework, addressing the inherently probabilistic nature of quantum devices, (ii) new randomized Bayesian experimental design techniques tailored for QDTs, capable of handling the complex dynamics and uncertainties in quantum systems, (iii) a robust generalized Bayesian framework using optimal transportation theory with adaptive prior and model enrichment mechanisms, enabling QDTs to detect and correct their flaws while minimizing system downtime, and (iv) advanced risk-neutral techniques for quantum optimal control and validation, improving QDTs' ability to generate high-fidelity quantum gates. The project also integrates these algorithms and methods into existing open-source software products, demonstrating and disseminating the developed QDTs.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." diff --git a/Geometric-Analysis/Awards-Geometric-Analysis-2024.csv b/Geometric-Analysis/Awards-Geometric-Analysis-2024.csv index c63f495..9bd07e1 100644 --- a/Geometric-Analysis/Awards-Geometric-Analysis-2024.csv +++ b/Geometric-Analysis/Awards-Geometric-Analysis-2024.csv @@ -1,13 +1,15 @@ "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract" +"2414532","Conference: Poisson 2024 Summer School and Conference","DMS","GEOMETRIC ANALYSIS","09/01/2024","08/19/2024","Ana Balibanu","LA","Louisiana State University","Standard Grant","Christopher Stark","08/31/2025","$17,000.00","","ana@math.lsu.edu","202 HIMES HALL","BATON ROUGE","LA","708030001","2255782760","MPS","126500","7556, 9150","$0.00","The Poisson 2024 Summer School and Conference will take place July 1-12, 2024 in Naples, Italy at the headquarters of the Accademia Pontaniana at the University of Naples. Poisson geometry is a highly interdisciplinary field which has found numerous applications
both to mathematics and to many areas of physics. The goal of Poisson 2024 is to make the latest developments in the field accessible to participants at all career stages, initiating an active exchange of ideas and giving them an opportunity to form new collaborations. The first week of this program will consist of a summer school of five minicourses delivered by senior experts, whose goal is to introduce junior researchers to a broad range of topics in some of the most active areas of Poisson geometry. The second week will feature a research conference with twenty talks by leading researchers and early-career emerging experts that will highlight recent breakthroughs. The purpose of this award is to support the participation of US-based researchers, especially those at an early career stage, in this international event.

The program of the meeting will survey the latest progress in a broad range of areas with links to Poisson geometry. The summer school will have a strong training component that features both introductory courses in Dirac geometry and shifted symplectic geometry as well as more advanced surveys of deformation quantization, mathematical physics, and quantum groups. The conference will include talks on a variety of rapidly developing research topics, including symplectic and Dirac geometry, generalized complex structures, Lie algebroids and Lie groupoids, geometric mechanics, Poisson algebraic geometry, integrable systems, higher structures, non-commutative geometry, quantum groups, and rapidly developing areas of Poisson-Lie groups and cluster theory. During the opening of the conference, the winners of the Andre Lichnerowicz prize for notable early-career contributions to Poisson geometry will also be announced. More details can be found at https://sites.google.com/view/poisson2024/poisson-2024.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405291","The ghost algebra for correlation functions of Anosov representations and the Weil Petersson gradient flow for renormalized volume","DMS","GEOMETRIC ANALYSIS","08/15/2024","08/07/2024","Martin Bridgeman","MA","Boston College","Standard Grant","Eriko Hironaka","07/31/2027","$282,000.00","","bridgem@bc.edu","140 COMMONWEALTH AVE","CHESTNUT HILL","MA","024673800","6175528000","MPS","126500","","$0.00","A topological surface is a space which is allowed to change its shape by stretching but without tearing. Understanding the geometry of the collection of these possible shapes, called the moduli space of the surface, has applications in a number of subfields of math and physics. Expanding on previous work, the PI will investigate properties of a particular flow on the moduli space that minimizes the distortions in a controllable way. This work is at the intersection of math and physics and is expected to lead to new connections between the two fields. The project will also introduce a new tool called the ghost algebra which allows one to track and extract properties of variations of quantities such as lengths. This grant will support graduate students in their research and travel, as well as the PI?s mentoring of graduate students and postdoctoral researchers. The PI will also co-organize conferences and workshops to support the career development of junior researchers. The findings from this research will be shared widely through conferences and seminars, fostering new connections between mathematics and physics.

This project has two main areas of study 1) the ghost algebra for correlation functions of Anosov representations and 2) the Weil Petersson gradient flow for renormalized volume. In the first, the PI and collaborators will study the symplectic structure of Higher Teichmüller spaces via the Hamiltonian flows of correlation functions by introducing a new combinatorial object called the ghost bracket on the ghost algebra of ghost polygons that allows one to compute Poisson brackets of correlation functions. In renormalized volume, the PI and collaborators will continue their program to use the Weil-Petersson gradient flow of renormalized volume to study the structure of hyperbolic three-manifolds. This program has been very successful culminating in recently completely describing the flow for acylindrical manifolds and relatively acylindrical manifolds. This sets the stage to attack the general case which will occupy the majority of this part of the research program.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2404705","Curves, Complexity, and Configurations","DMS","GEOMETRIC ANALYSIS","08/15/2024","08/07/2024","Jayadev Athreya","WA","University of Washington","Standard Grant","Eriko Hironaka","07/31/2027","$278,000.00","","jathreya@uw.edu","4333 BROOKLYN AVE NE","SEATTLE","WA","981951016","2065434043","MPS","126500","","$0.00","The objectives of this project are to answer a series of fundamental questions about the geometry and dynamics of surfaces, motivated by questions originating in physics and materials science, in particular the theories of kinetic motion and of electron transport.The intellectual merit and broader impacts in this proposal inform each other via engagement with students at all levels and a commitment to diversity in teaching, mentoring, public engagement, and professional service activities associated to this project.

This project has three main themes, centering on the geometry and dynamics of surfaces. The first is to develop a theory of Eisenstein series and cusp forms for the moduli space of translation surfaces, drawing inspiration from classical number theory, to unify and strengthen important geometric and dynamical results for renormalization dynamics on the moduli spaces of translation surfaces. The second thread, inspired by the study of special trajectories on polygonal billiards, focuses on the relationship between combinatorial complexity (informally, the number of bounces for a billiard trajectory) and geometric length of saddle connections on translation surfaces, and in particular, proving precise asymptotic results for new families of translation surfaces beyond flat tori. The third thread considers the general geometry and counting problems associated to configurations of curves and graphs on translation and hyperbolic surfaces.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2349566","Conference: Groups Actions and Rigidity: Around the Zimmer Program","DMS","GEOMETRIC ANALYSIS","04/01/2024","08/08/2024","David Fisher","TX","William Marsh Rice University","Standard Grant","Swatee Naik","03/31/2025","$43,568.00","Kathryn Mann, Aaron Brown","df32@rice.edu","6100 MAIN ST","Houston","TX","770051827","7133484820","MPS","126500","7556","$0.00","This NSF award provides support for US based participants to attend a sequence of workshops, to be held at Centre Internationale de Rencontres mathematique in Marseilles and the Insitut Henri Poincare in Paris in April-July 2024. These workshops are held in conjunction with a special semester Group actions and Rigidity: Around the Zimmer Program at IHP during this period. The goal of both the workshops and special semester are to bring together specialists working in a related cluster of timely and important topics in dynamics and geometry related to, actions of large groups or spaces with lots of symmetries. The primary purpose of the award is to provide travel funding to allow early career scholars from the US to participate in the workshops and the semester program.

Highly symmetric manifolds traditionally play a central role in mathematics, ranging from number theory to dynamics to geometry. This research topic centers on a program put forward by Zimmer and Gromov to study manifolds with large groups of symmetries, with the general idea that such manifolds should arise from natural algebraic and geometric constructions. Investigations in this area are often spurred by sudden discovery of or deepening of connections to other areas of mathematics. Recent new developments have been occurring with breakneck speed. Particularly important have been deepening connections to low dimensional topology, to homogeneous and hyperbolic dynamics as well as novel connections to operator algebras, and to classical work on characterizations of Lie groups among connected topological groups. The concentrated activity around this special term and the workshops funded in part by this grant are needed to capture this momentum and spur further progress. Information about individual workshops and meetings can be found at https://indico.math.cnrs.fr/event/9043/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405274","Potential theoretic aspects of complex geometry","DMS","GEOMETRIC ANALYSIS","09/01/2024","08/02/2024","Tamas Darvas","MD","University of Maryland, College Park","Standard Grant","Qun Li","08/31/2027","$204,372.00","","tdarvas@math.umd.edu","3112 LEE BUILDING","COLLEGE PARK","MD","207425100","3014056269","MPS","126500","","$0.00","Potential theory has its roots in classical physics and the realization that gravity and the electrostatic force can be described using so-called potential functions, both of which satisfy Poisson's equation. In more recent decades, potential theory has been recognized as ubiquitous in many different areas of mathematics and physics. This project seeks to understand the role of potential theory in complex geometry. Broadly speaking, complex geometry aims to find ideal geometric models that are simple enough to model the physical universe, describing interactions between small particles, or even colliding galaxies. The PI will also train graduate students in the subject area, and introduce undergraduates to this field through summer research programs, in each case focusing on providing opportunities to traditionally underrepresented members of academia. On the outreach side, the PI will continue to make educational videos disseminated online, as well as give popular science lectures in local middle schools.

Complex geometry is the discipline at the intersection of differential and algebraic geometry. As advocated by Demailly, Siu, and others, it is possible to study this subject using potential-theoretic methods. Along these lines, the PI plans to make significant progress on a cluster of interconnected questions and conjectures in complex geometry by employing a combination of methods from potential theory, infinite-dimensional geometry, and more traditional methods of geometric analysis. There is a vast literature on Kähler quantization for smooth metrics. Instead, the PI will study quantization in the context of finite energy potential theory that accommodates degenerate Kähler metrics. Potential applications range from the quantization of Radon measures to Yau-Tian-Donaldson type theorems. The PI will also study the fascinating connections between convex and complex geometry in the transcendental context. This includes establishing a link between the Hausdorff geometry of convex bodies and the geometry of singularity types of quasiplurisubharmonic functions, and better understanding the complex Brunn-Minkowski inequality of Berndtsson, leading to uniqueness theorems for degenerate canonical Kähler metrics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2404790","Quantitative symplectic geometry and dynamics","DMS","GEOMETRIC ANALYSIS","08/01/2024","08/01/2024","Michael Hutchings","CA","University of California-Berkeley","Standard Grant","Swatee Naik","07/31/2027","$300,000.00","","hutching@math.berkeley.edu","1608 4TH ST STE 201","BERKELEY","CA","947101749","5106433891","MPS","126500","","$0.00","This project will facilitate development of new tools to study mathematical questions related to how physical systems evolve in time. A state of the system corresponds to a point in an even dimensional phase space, and the system evolves along an odd dimensional energy level in the phase space. A particular focus will be placed on understanding the existence and properties of periodic orbits, which describe behavior that repeats in time, especially in the case when the phase space is four dimensional and the energy level is three dimensional. The geometry of the phase space will also be studied, developing methods to determine when one dynamical system is equivalent to another one by a change of coordinates. Various research projects on these topics will provide research training for graduate students in the latest techniques in symplectic geometry and related areas of mathematics. The PI will also engage in multiple outreach activities.

Specific projects include the following. Filtrations on embedded contact homology will be studied with the goal of proving in full generality that every contact form on a closed three-manifold has either two or infinitely many simple Reeb orbits. Knot filtered embedded contact homology will be studied with applications to symplectic cobordisms between transverse knots. Symplectic invariants of open domains arising from barcodes in equivariant symplectic homology will be used to classify some open domains up to symplectomorphism. Closing lemmas will be extended to more general vector fields than Reeb vector fields in three dimensions. Universal quantitative invariants will be developed with applications to symplectic embedding problems, constraints on Lagrangian submanifolds, refinements of the Arnold chord conjecture, elementary spectral invariants of contact manifolds, and comparisons between symplectic capacities.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2422900","Spectral Asymptotics of Laplace Eigenfunctions","DMS","GEOMETRIC ANALYSIS","03/01/2024","03/11/2024","Emmett Wyman","NY","SUNY at Binghamton","Standard Grant","Joanna Kania-Bartoszynska","07/31/2025","$61,364.00","","emmett.wyman@rochester.edu","4400 VESTAL PKWY E","BINGHAMTON","NY","139024400","6077776136","MPS","126500","","$0.00","The research project falls within the field of spectral asymptotics, which studies the behavior of high-frequency Laplace eigenfunctions on manifolds (surfaces and spaces with curvature). The physical analogues of eigenfunctions are standing waves, and the eigenvalues may be thought of as their corresponding frequencies. The interdependence between high-frequency eigenfunctions and the geometry of the manifold on which they live is central to a broad range of fields from quantum physics to number theory. Indeed, eigenfunctions are steady-state solutions to the Schrödinger equation, and their eigenvalues are the corresponding energies. To illustrate the connection to number theory, the task of accurately counting the number of eigenfunctions of a given frequency on the flat torus is equivalent to counting the number of ways an integer can be expressed as the sum of, say, two squares. This project aims to develop new tools to advance understanding in spectral asymptotics, whose interconnectedness to seemingly disparate areas of mathematics and science make its study particularly valuable.

As part of the research project, the PI intends to develop and use tools from microlocal analysis and the theory of Fourier integral operators to refine a variety of formulas describing the behavior of high-frequency eigenfunctions, and in particular describing what effect the underlying geometry has on these formulas. The PI intends to make advancements towards a conjecture on the remainder term of the Weyl law for products of manifolds, to develop a general multilinear theory of Fourier integral operators for use in both spectral asymptotics and geometric measure theory, and to further explore the connection between spectral quantities and the presence of corresponding geometric configurations in the manifold.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2438372","Conference: Frontiers in Sub-Riemannian Geometry","DMS","GEOMETRIC ANALYSIS","11/01/2024","08/02/2024","Aissa Wade","PA","Pennsylvania State Univ University Park","Standard Grant","Qun Li","10/31/2025","$12,186.00","","wade@math.psu.edu","201 OLD MAIN","UNIVERSITY PARK","PA","168021503","8148651372","MPS","126500","7556","$0.00","The international conference ""Frontiers in Sub-Riemannian Geometry"" will be held at the CIRM, Marseille (France) during the week of November 25-29, 2024. The aim of the conference is to bring together researchers working in different areas of mathematics related to sub-Riemannian geometry, with different backgrounds, to share the most recent results with multiple points of view and so to foster interactions between research groups and to contribute to the training of young researchers. This award will provide support for U.S. based participants.

Sub-Riemannian geometry has grown significantly since the early 1990?s. It is closely related to several areas in mathematics such as geometric control theory, the theory of partial differential equations, geometric measure theory, etc. Sub-Riemannian geometry also plays a major role in many mathematical applications such as robotics, quantum control, and neurogeometry. For more details, see the website: https://conferences.cirm-math.fr/3091.html

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2405328","Einstein Metrics and Ricci Flows in Dimension 4","DMS","GEOMETRIC ANALYSIS","08/15/2024","08/02/2024","Tristan Ozuch-Meersseman","MA","Massachusetts Institute of Technology","Standard Grant","Qun Li","07/31/2027","$200,000.00","","ozuch@mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","126500","","$0.00","Topology is a branch of mathematics that is concerned with the shape of a space. Two-dimensional surfaces are topologically characterized by the number of holes within, a simple notion of complexity. Optimizing geometry helps to better understand the underlying topology; for example, flattening a crumpled sheet of paper or untying a balloon animal makes it easier to count their holes. Ricci flow, a geometric optimization technique, searches for optimal geometries called Einstein manifolds, generalizing flat planes and round spheres. This flow provides an algorithmic approach to decomposing three-dimensional geometries and has been used to characterize topologies in dimension three. While challenges in dimension five have been addressed through systematic methods, the final frontier is dimension four, where Einstein manifolds have been extensively studied in physics. This project aims to further study Einstein four-manifolds while developing a new, four-dimensional-specific theory of Ricci flow. It will bring together researchers from analysis, geometry, topology, and physics. The PI will involve undergraduate and graduate students in the project and integrate research questions into teaching and advising.

This project aims to understand and construct 4-dimensional Einstein metrics and Ricci flows. The main difficulties are singularities, where topological surgeries occur, specifically ""orbifold"" singularities, ""cusp"" formation, and collapsing. The PI will continue studying these degenerations, their stability, and their links to additional structures such as a Kähler one. Most results about Ricci flows are either 3-dimensional or apply to any n-dimension, with few focusing on the specifics of dimension 4, where most topological questions remain open. Through his extensive study of Einstein 4-manifolds, the PI is familiar with the rich set of 4-dimensional techniques developed over decades. He aims to apply these techniques to study Ricci flows and their singularities, focusing on the topological content of the three types of degenerations: orbifold singularities, cusp formation, and collapsing.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405104","Hyperbolic geometry in dimensions 2 and 3","DMS","GEOMETRIC ANALYSIS","08/01/2024","07/31/2024","Kenneth Bromberg","UT","University of Utah","Standard Grant","Eriko Hironaka","07/31/2027","$285,000.00","","bromberg@math.utah.edu","201 PRESIDENTS CIR","SALT LAKE CITY","UT","841129049","8015816903","MPS","126500","","$0.00","Two and three-dimensional spaces are fundamental objects lying at the intersection of many branches of mathematics. One approach to studying these spaces is to endow them with geometric structure and then use the geometry to study the spaces. The three most familiar geometries are the classical Euclidean or flat geometry, and the two non-Euclidean geometries: spherical and hyperbolic. It has been known since the late 1800s that most two-dimensional spaces (or surfaces) exhibit hyperbolic geometry. Thurston's groundbreaking work in the 1970s showed that ""most"" three dimensional spaces (or three-manifolds) also have hyperbolic geometry. The rich landscape of hyperbolic manifolds in two and three dimensions motivates this project's focus on hyperbolic geometry. The project will include many sub-projects suitable for training graduate students to work in this area.

The PI, together with graduate students, will study questions around the geometry of hyperbolic 3-manifolds. One central topic will be the ""renormalized volume"" of a hyperbolic 3-manifold, and the connection between the Weil-Petersson gradient flow and the volume of the convex core. While renormalized volume has strong connections to physics, in this project the focus will be mathematical. The PI will study a version of renormalized volume of the universal Teichmüller space, and Thurston's skinning map. In another series of projects, the PI will study a family of curve complexes that interpolates between the usual curve graph and a quasi-tree, and will investigate the existence of actions of the mapping class group on median spaces and CAT(0) cube complexes.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2404915","Variational methods in singular geometry","DMS","GEOMETRIC ANALYSIS","09/01/2024","07/31/2024","Georgios Daskalopoulos","RI","Brown University","Standard Grant","Qun Li","08/31/2027","$220,000.00","","daskal@math.brown.edu","1 PROSPECT ST","PROVIDENCE","RI","029129100","4018632777","MPS","126500","9150","$0.00","Many physical phenomena can be described by the principle of least action. This involves studying minima of certain functionals, called Lagrangians, named after the French mathematician and astronomer J-L Lagrange (1736-1813), that describe the energy of the system under consideration. For example, it is possible to derive Newton's laws of classical mechanics from the principle of least action. The principle can be applied also to more complicated systems, even infinite dimensional configuration spaces. One famous such example is the case of geodesics, paths minimizing the distance between two points in a smooth space. Another, more involved example is the case of harmonic maps. Here the Lagrangian energy is the total stretch of a map between two smooth spaces. In this project the PI proposes to study analogous situations for more complicated Lagrangians that have important applications. The project has also an educational component where the PI is planning to supervise graduate students towards their Ph.D. theses, undergraduates through seminar courses, and write expository notes for a wider audience.

In slightly more technical terms, harmonic maps are critical points of the L-2 norm of the gradient (Dirichlet integral) of a map between two Riemannian manifolds. The PI proposes to study the calculus of variations of functionals associated with other function space norms like the L-infinity and L-1 norms. Minimizing functionals associated to the L-infinity norm yield solutions of fully non-linear degenerate elliptic PDE?s with very challenging regularity properties. Similarly, solutions of the dual non-linear problem for functionals involving the L-1 norm are equally challenging. The singular sets of these solutions provide geometric realizations of topological objects, like geodesic foliations and laminations, studied in topology. The PI proposes to develop the analytic methods to study these topological objects as well as others studied in Thurston theory. Examples are earthquakes and cataclysms. There is very little known in the literature about the analytic underpinnings of the theory so the PI has to develop most of the techniques from scratch.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2438372","Conference: Frontiers in Sub-Riemannian Geometry","DMS","GEOMETRIC ANALYSIS","11/01/2024","08/02/2024","Aissa Wade","PA","Pennsylvania State Univ University Park","Standard Grant","Qun Li","10/31/2025","$12,186.00","","wade@math.psu.edu","201 OLD MAIN","UNIVERSITY PARK","PA","168021503","8148651372","MPS","126500","7556","$0.00","The international conference ""Frontiers in Sub-Riemannian Geometry"" will be held at the CIRM, Marseille (France) during the week of November 25-29, 2024. The aim of the conference is to bring together researchers working in different areas of mathematics related to sub-Riemannian geometry, with different backgrounds, to share the most recent results with multiple points of view and so to foster interactions between research groups and to contribute to the training of young researchers. This award will provide support for U.S. based participants.

Sub-Riemannian geometry has grown significantly since the early 1990?s. It is closely related to several areas in mathematics such as geometric control theory, the theory of partial differential equations, geometric measure theory, etc. Sub-Riemannian geometry also plays a major role in many mathematical applications such as robotics, quantum control, and neurogeometry. For more details, see the website: https://conferences.cirm-math.fr/3091.html

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2405328","Einstein Metrics and Ricci Flows in Dimension 4","DMS","GEOMETRIC ANALYSIS","08/15/2024","08/02/2024","Tristan Ozuch-Meersseman","MA","Massachusetts Institute of Technology","Standard Grant","Qun Li","07/31/2027","$200,000.00","","ozuch@mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","126500","","$0.00","Topology is a branch of mathematics that is concerned with the shape of a space. Two-dimensional surfaces are topologically characterized by the number of holes within, a simple notion of complexity. Optimizing geometry helps to better understand the underlying topology; for example, flattening a crumpled sheet of paper or untying a balloon animal makes it easier to count their holes. Ricci flow, a geometric optimization technique, searches for optimal geometries called Einstein manifolds, generalizing flat planes and round spheres. This flow provides an algorithmic approach to decomposing three-dimensional geometries and has been used to characterize topologies in dimension three. While challenges in dimension five have been addressed through systematic methods, the final frontier is dimension four, where Einstein manifolds have been extensively studied in physics. This project aims to further study Einstein four-manifolds while developing a new, four-dimensional-specific theory of Ricci flow. It will bring together researchers from analysis, geometry, topology, and physics. The PI will involve undergraduate and graduate students in the project and integrate research questions into teaching and advising.

This project aims to understand and construct 4-dimensional Einstein metrics and Ricci flows. The main difficulties are singularities, where topological surgeries occur, specifically ""orbifold"" singularities, ""cusp"" formation, and collapsing. The PI will continue studying these degenerations, their stability, and their links to additional structures such as a Kähler one. Most results about Ricci flows are either 3-dimensional or apply to any n-dimension, with few focusing on the specifics of dimension 4, where most topological questions remain open. Through his extensive study of Einstein 4-manifolds, the PI is familiar with the rich set of 4-dimensional techniques developed over decades. He aims to apply these techniques to study Ricci flows and their singularities, focusing on the topological content of the three types of degenerations: orbifold singularities, cusp formation, and collapsing.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2402129","Positive curvature and torus symmetry","DMS","GEOMETRIC ANALYSIS","08/01/2024","08/01/2024","Lee Kennard","NY","Syracuse University","Standard Grant","Qun Li","07/31/2027","$292,481.00","","ltkennar@syr.edu","900 S CROUSE AVE","SYRACUSE","NY","13244","3154432807","MPS","126500","","$0.00","As a mathematician faced with a research problem or an educational task, the PI strives to abstract away inessential information, break down complicated structures into simple components, and identify the right tools for the job. In this project, the PI plans to apply methods from disparate fields such as discrete mathematics and homotopy theory to problems in geometry, especially problems involving the impact of symmetry and local curvature conditions on the global shape of high-dimensional objects called manifolds. Crucial to this progress are communication and collaboration with experts from across the country and around the globe whose areas of expertise both overlap and supplement the PI?s. Additional aspects of this project include growing and diversifying the body of students, researchers, and experts in STEM fields who will positively impact the advancement of the research goals of this project, the future of STEM education, and our society?s ability more broadly to tackle difficult scientific problems.

The PI will analyze local-to-global principles in geometry. Goals involve analyzing the interaction of (local) positive curvature conditions in Riemannian geometry and (global) algebraic topological and symmetric structures. The PI will apply tools from homotopy theory, equivariant cohomology theory, matroid theory, and topological graph theory. These methods have applications in the Grove Symmetry Program but do not use curvature, so this work has the potential to apply in other areas of geometry.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405114","Unstable minimal surfaces and applications","DMS","GEOMETRIC ANALYSIS","08/01/2024","08/01/2024","Daniel Ketover","NJ","Rutgers University New Brunswick","Standard Grant","Qun Li","07/31/2027","$235,375.00","","dk927@scarletmail.rutgers.edu","3 RUTGERS PLZ","NEW BRUNSWICK","NJ","089018559","8489320150","MPS","126500","","$0.00","Minimal surfaces, often modeled by soap films, are shapes in equilibrium first studied by Lagrange in the 1700s. Such surfaces locally minimize area and appear everywhere in nature? in chemistry, materials science, biology, and general relativity. In mathematics, they have been applied more recently to solve problems in Geometry and Topology, such as the Poincaré Conjecture, the Willmore conjecture, and more recently to prove the Smale Conjecture in many spherical space-forms. The PI will work to discover new minimal surfaces which are not area-minimizing (and thus very difficult to find in nature) - but which can have other major applications in Geometry. In addition to this research, the PI will focus on teaching and training of undergraduate and graduate students as well as advancing the field by organizing conferences, conducting mini-courses for graduate students, writing expository materials and working toward making a computational study of minimal surfaces accessible to the wider mathematical public.

More precisely, the objectives of this project are to develop new techniques to study min-max minimal surfaces obtained from high-parameter sweep-outs as well as find further applications in Topology and Geometry. Recently the PI used a two-parameter sweepout to construct long-conjectured singularity models of the mean curvature flow (MCF), and he will further study the geometry and properties of these new examples. In particular, the relationship between minimal surfaces in the shrinker metric and expander metric will be explored in light of Ilmanen?s Genus Reduction Conjecture, asserting that the genus of a surface at a singularity of the MCF must strictly drop. The PI will more generally use min-max and flow methods to show that the lowest genus stabilization of two irreducible splittings is realized by an index 2 minimal surface addressing a conjecture of D. Bachman. Higher-parameter families will be used to prove the Goeritz-Powell Conjecture asserting, roughly speaking, that the fundamental group of the space of genus g Heegaard surfaces in the three-sphere is finitely generated. The PI will also obtain multiplicity one results as well as sharp index estimates in the min-max theory in the case of stable surfaces.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2404195","Differential Equations and the Geometry of Manifolds","DMS","GEOMETRIC ANALYSIS","08/01/2024","08/01/2024","Jeff Viaclovsky","CA","University of California-Irvine","Standard Grant","Qun Li","07/31/2027","$223,343.00","","jviaclov@uci.edu","160 ALDRICH HALL","IRVINE","CA","926970001","9498247295","MPS","126500","","$0.00","An important motivation for the research of the PI is to understand the relationship between the geometry and the topology of a space. The latter, topology, is the study of properties of a space which are invariant under continuous stretching or bendings of a space, while the former, geometry, involves understanding distances and is more rigid. For example, the surface of our planet is a sphere, and one measures distances on it by computing arclengths of great circles (the Earth is actually an oblate spheroid, but it is very close to being perfectly spherical). One can imagine deforming the Earth by pushing in or pulling on small or large regions to warp the geometry. Such a deformation is less appealing that the familiar round Earth, and there are many ways to make this notion very precise in terms of minimizing some sort of total energy measurement. This is directly related to physical principles which say that the state of a physical system will tend towards a final configuration which minimizes the total energy. This idea can be generalized to higher-dimensional objects called manifolds, which are generalized versions of the surface of our planet. For example, the space that we live in is three-dimensional, and if one includes time, we are in a four-dimensional universe. In order to understand these types of higher-dimensional objects, one attempts to find the best way to measure distances on them which use the least amount of energy, and maximize the symmetries of the space. The projects supported by this award are to define appropriate energies on such spaces, and to seek out the important optimal geometries which minimize the total energy. The PI is committed to integrating research and education and cultivating intellectual development on many levels, and plans to continue to be active in outreach and organization of conferences and other events in the mathematics community.

In more technical terms, the research of the PI is, broadly speaking, to use solutions of partial differential equations which are geometric in origin to study properties of differentiable manifolds. The main areas of concentration of the PI's research are the classification of gravitational instantons in dimension four, understanding Gromov-Hausdorff limits of Einstein metrics in the collapsing case, and the study of higher-dimensional complete non-compact Calabi-Yau structures. The PI has contributed to the classification of gravitational instantons in dimension 4, and plans to further investigate the global structure of the moduli spaces of these metrics. The PI has also contributed to the classification of asymptotically Calabi Calabi-Yau structures, and plans to study other types of complete non-compact Calabi-Yau structures in higher dimensions. The PI has contributed to the understanding of Gromov-Hausdorff limits of Calabi-Yau metrics on compact manifolds, and plans to further study global properties of compactifications of such moduli spaces.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -25,7 +27,6 @@ "2337451","CAREER: Higgs bundles and Anosov representations","DMS","ALGEBRA,NUMBER THEORY,AND COM, GEOMETRIC ANALYSIS","07/01/2024","02/02/2024","Brian Collier","CA","University of California-Riverside","Continuing Grant","Swatee Naik","06/30/2029","$79,647.00","","brian.collier@ucr.edu","200 UNIVERSTY OFC BUILDING","RIVERSIDE","CA","925210001","9518275535","MPS","126400, 126500","1045","$0.00","This project focuses on the mathematical study of curved surfaces by connecting algebraic objects to them and thereby generalizing the scope of their application. One of the main notions used is that of a surface group representation, a concept which connects surfaces to generalizations of classical geometries such as Euclidean and hyperbolic geometry. The study of surfaces has surprising applications throughout many fields of mathematics and physics. Consequently, the project lies at the intersection of multiple disciplines. In addition to cutting edge mathematical research, the project will promote the progress of science and mathematics through different workshops aimed at graduate students as well as community outreach events. The educational component will also focus on creating an engaging and inclusive place for mathematical interactions for students and early career researchers.

In the past decades, both the theories of Higgs bundles and Anosov dynamics have led to significant advancements in our understanding of the geometry of surface groups. Recent breakthroughs linking these approaches are indirect and mostly involve higher rank generalizations of hyperbolic geometry known as higher rank Teichmuller spaces. The broad aim of this project is to go beyond higher rank Teichmuller spaces by using Higgs bundles to identify subvarieties of surface group representations which generalize the Fuchsian locus in quasi-Fuchsian space. The cornerstone for the approach is the role of Slodowy slices for Higgs bundles. Specifically, the PI aims to establish Anosov properties of surface group representations associated to Slodowy slices in the Higgs bundle moduli space. This approach will significantly extend applications of Higgs bundles to both Anosov representations and (G,X) geometries. It will complete the component count for moduli of surface group representations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350508","Conference: Noncommutative Geometry and Analysis","DMS","GEOMETRIC ANALYSIS","03/01/2024","01/05/2024","Antoine Song","CA","California Institute of Technology","Standard Grant","Swatee Naik","02/28/2025","$30,000.00","Zhongshan An, Zhizhang Xie, Simone Cecchini","aysong@caltech.edu","1200 E CALIFORNIA BLVD","PASADENA","CA","911250001","6263956219","MPS","126500","7556","$0.00","This award provides support for the 2024 Workshop in Noncommutative Geometry and Analysis that will be held at the California Institute of Technology, March 11 - 13, 2024. This is the next iteration of the annual workshop series, which began in 2022. The main goal of the workshop is to foster scientific and social interaction among early career mathematicians in various branches of mathematics, ranging from noncommutative geometry to geometric analysis. Recent advances in and interactions between these fields have given rise to a growing need for such a meeting specifically dedicated to these topics. This event is designed to have a relatively small number of participants, and it will provide a valuable platform for graduate students and postdocs to engage with current research frontiers in these areas.

Many of the recent developments in noncommutative geometry, index theory, geometric analysis and mathematical physics have focused on problems related to scalar curvature, minimal surfaces, and mathematical general relativity. The main goal of this workshop is to promote a better understanding of those latest developments and their interrelationships. A recent program concerning scalar curvature has given rise to new perspectives and inspired a wave of recent activity in this area. The theory of minimal surfaces has made significant strides on old questions pertaining to regularity or existence questions, while uncovering new problems related to adjacent fields. In the field of general relativity, results using harmonic maps have improved our understanding of the classical Positive Mass Theorem. This workshop aims to facilitate communication among participants from those diverse fields, fostering opportunities for potential collaboration. More information is available at the workshop webpage, https://sites.google.com/view/ymncga-2024/home

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350239","Conference: Symmetry and Geometry in South Florida","DMS","GEOMETRIC ANALYSIS","02/15/2024","11/30/2023","Anna Fino","FL","Florida International University","Standard Grant","Qun Li","01/31/2025","$26,366.00","Gueo Grantcharov, Michael Jablonski, Samuel Lin","afino@fiu.edu","11200 SW 8TH ST","MIAMI","FL","331992516","3053482494","MPS","126500","7556","$0.00","The conference ?Symmetry and Geometry in South Florida? will take place at Florida International University, Miami, from February 16 to 18, 2024. This conference will serve the region of the southeastern United States, especially South Florida, and it will expose participants to cutting-edge research in Riemannian Geometry. Being organized around the principle of inclusiveness, the organizers will promote the conference to women and under-represented groups so as to increase their participation in the meeting. The meeting will feature a diverse array of speakers, including graduate students, postdocs, and established researchers.

Symmetry has been an essential tool in the development of differential geometry; it has been used to create crucial examples and to test special cases of general conjectures. Although symmetry is a widely used tool, the techniques involved can look substantially different across sub-fields. Given its exceptional nature, the organizers will host a conference centered around the theme of symmetry. The meeting aims to disseminate cutting-edge techniques and applications of group actions from across a broad spectrum of sub-disciplines inside differential geometry, including spectral geometry, curvature bounds, homogeneous spaces, and geometric flows. The conference also includes shorter talks by graduate students and younger researchers to showcase their work.
The link to the webpage to the conference is

https://sites.google.com/view/sgsf-2024/home-page?pli=1

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2349566","Conference: Groups Actions and Rigidity: Around the Zimmer Program","DMS","GEOMETRIC ANALYSIS","04/01/2024","12/18/2023","David Fisher","TX","William Marsh Rice University","Standard Grant","Swatee Naik","03/31/2025","$35,000.00","Kathryn Mann, Aaron Brown","df32@rice.edu","6100 MAIN ST","Houston","TX","770051827","7133484820","MPS","126500","7556","$0.00","This NSF award provides support for US based participants to attend a sequence of workshops, to be held at Centre Internationale de Rencontres mathematique in Marseilles and the Insitut Henri Poincare in Paris in April-July 2024. These workshops are held in conjunction with a special semester Group actions and Rigidity: Around the Zimmer Program at IHP during this period. The goal of both the workshops and special semester are to bring together specialists working in a related cluster of timely and important topics in dynamics and geometry related to, actions of large groups or spaces with lots of symmetries. The primary purpose of the award is to provide travel funding to allow early career scholars from the US to participate in the workshops and the semester program.

Highly symmetric manifolds traditionally play a central role in mathematics, ranging from number theory to dynamics to geometry. This research topic centers on a program put forward by Zimmer and Gromov to study manifolds with large groups of symmetries, with the general idea that such manifolds should arise from natural algebraic and geometric constructions. Investigations in this area are often spurred by sudden discovery of or deepening of connections to other areas of mathematics. Recent new developments have been occurring with breakneck speed. Particularly important have been deepening connections to low dimensional topology, to homogeneous and hyperbolic dynamics as well as novel connections to operator algebras, and to classical work on characterizations of Lie groups among connected topological groups. The concentrated activity around this special term and the workshops funded in part by this grant are needed to capture this momentum and spur further progress. Information about individual workshops and meetings can be found at https://indico.math.cnrs.fr/event/9043/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2428771","RUI: Configuration Spaces of Rigid Origami","DMS","GEOMETRIC ANALYSIS","04/15/2024","04/22/2024","Thomas Hull","PA","Franklin and Marshall College","Continuing Grant","Christopher Stark","08/31/2025","$59,029.00","","thull1@fandm.edu","415 HARRISBURG AVE","LANCASTER","PA","176032827","7173584517","MPS","126500","9229","$0.00","Origami, the art of paper folding, has been practiced for centuries. The mathematics behind origami, however, is not yet fully understood. In particular, some origami models can be folded and unfolded in such a way that we could make the crease lines be hinges and the paper between them stiff like sheet metal. Such models are called rigidly flexible origami and have applications that span the physical and biological sciences, ranging from unfolding solar sails to collapsible heart stents. This project will add mathematical tools that allow industrial applications to employ cutting-edge research, from large-scale architectural structures to nano-scale robotics driven by origami mechanics. The tools from this project will help design self-foldable structures. Currently self-folding designs in engineering, architecture, and the biological sciences involve building physical models in a trial-and-error approach, wasting time and resources. The self-folding research provided by this project will allow designers to avoid pitfalls and tighten the design-to-realization process significantly. In addition to the research component, the PI shall organize a diverse range of educational activities including in-service teacher training and education, undergraduate mentoring and preparation for graduate school; high-school and undergraduate classes on the mathematics of folding; for the public, general-audience articles, lectures, and exhibitions. This will increase interest in STEM fields through the fun, hands-on nature of origami while simultaneously disseminating project results.

The methods of this project involve a blend of practical experimentation with theory. Programmed self-foldability of structures will be achieved by trimming away undesired paths from the configuration space of all possible rigid foldings. One approach is to transform a given rigid folding of a crease pattern into a kinematically equivalent rigid folding with fewer degrees of freedom. The PI has proposed such a transform and will develop others. Key to all of this, however, is gaining a better understanding of rigid origami configuration spaces, which are algebraically complicated and not well understood. The project seeks to understand, and exploit, local-to-global behavior that is present in many known examples of rigid origami. In these examples approximating the configuration space near the origin (the unfolded state) leads to exact equations for the global configuration space. Formulating rigid origami configuration spaces in this way will add insight into the general field of flexible polyhedral surfaces, as well as provide the data needed to prove the feasibility of origami crease pattern transforms and design reliably self-foldable origami mechanisms.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2403981","Scalar Curvature, Optimal Transport, and Geometric Inequalities","DMS","GEOMETRIC ANALYSIS","07/01/2024","05/01/2024","Simon Brendle","NY","Columbia University","Standard Grant","Qun Li","06/30/2027","$254,266.00","","sab2280@columbia.edu","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","126500","","$0.00","This project focuses on questions at the intersection of differential geometry and the theory of partial differential equations. Differential geometry uses techniques from calculus to understand the shape and curvature of surfaces. These ideas can be generalized to higher-dimensional manifolds. In particular, they provide the mathematical framework for the Einstein equations in general relativity, which link the matter density to the curvature of space-time. A major theme in differential geometry has been to study the interplay between the curvature and the large-scale properties of a manifold. To study these questions, various techniques have been developed, many of them based on partial differential equations. Examples include the minimal surface equation and the partial differential equations governing optimal mass transport. This project is aimed at understanding these partial differential equations. This is of significance within mathematics. There are also connections with general relativity. Moreover, ideas from optimal transport have found important applications in statistics and computer science. The project also includes a variety of mentoring and outreach activities.

An important topic in geometry is to understand the geometric meaning of the scalar curvature. The PI recently obtained a new rigidity theorem for metrics with nonnegative scalar curvature on polytopes. The PI plans to extend that result to the more general setting of initial data sets satisfying the dominant energy condition. In another direction, the PI plans to work on geometric inequalities and optimal mass transport. On the one hand, the PI plans to use ideas from differential geometry and partial differential equations to study the behavior of optimal maps. On the other hand, the PI hopes to use ideas from optimal transport to prove new geometric inequalities. Ideas from optimal transport can be used to give elegant proofs of many classical inequalities, including the isoperimetric inequality and the sharp version of the Sobolev inequality. Moreover, the recent proof of the sharp isoperimetric inequality for minimal surfaces is inspired by optimal transport.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2415356","Conference: Yamabe Memorial Symposium","DMS","GEOMETRIC ANALYSIS","08/01/2024","07/01/2024","Erkao Bao","MN","University of Minnesota-Twin Cities","Standard Grant","Qun Li","07/31/2025","$25,000.00","Michelle Chu","bao@umn.edu","200 OAK ST SE","MINNEAPOLIS","MN","554552009","6126245599","MPS","126500","7556","$0.00","The 2024 Yamabe Memorial Symposium will be held at the School of Mathematics of the University of Minnesota - Twin Cities, from Friday, October 4th to Sunday, October 6th, 2024. The Yamabe Memorial Symposium is a prestigious biennial conference in geometry and topology, established in 1962. It is renowned among geometers and topologists for its high-level, cutting-edge talks, strong support for U.S. graduate students, and its ability to connect leading experts with junior researchers through well-organized events. This year, the symposium will uphold this tradition, offering a comprehensive exploration of various aspects of symplectic and contact geometry in light of recent breakthroughs in these fields.

Recent major breakthroughs include advancements in the foundations of Floer theory, such as the development of stable homotopy theory for Floer theory, the introduction of global Kuranishi charts, and their applications to the Arnold conjecture over integers. Additionally, Floer theory has been applied to symplectic topology, including the refutation of the simplicity conjecture. Complementary to Floer theory, significant progress has been made in the study of Hamiltonian torus actions and topological methods in higher-dimensional contact structures. Eight confirmed speakers, comprising leading experts from around the world, will ensure comprehensive coverage of these areas. The webpage for the Yamabe Symposium is https://cse.umn.edu/math/yamabe-memorial-symposium

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -34,8 +35,8 @@ "2419988","Conference: Groups, Logic, and Computation","DMS","ALGEBRA,NUMBER THEORY,AND COM, GEOMETRIC ANALYSIS, FOUNDATIONS","06/15/2024","06/11/2024","Alexander Ushakov","NJ","Stevens Institute of Technology","Standard Grant","Tim Hodges","05/31/2025","$18,000.00","Mahmood Sohrabi","sasha.ushakov@gmail.com","1 CASTLEPOINT ON HUDSON","HOBOKEN","NJ","07030","2012168762","MPS","126400, 126500, 126800","","$0.00","This award supports participation in the conference ?Groups, Logic, and Computation: Interactions between group theory, model theory, and computer science"" that will be held at the Stevens Institute of Technology (New Jersey), June 12-14, 2024. The event will bring researchers from various branches of group theory, model theory, and computer science together to work on some of the many open questions in the field that are now being studied from fresh and promising perspectives; it will further strengthen the connections the field has to other branches of mathematics. This exchange of ideas among experts, students, and postdocs aims to disseminate current knowledge and identify promising directions for further progress.

The conference will be devoted to developments in group theory focusing on groups and group actions as well as other areas of mathematics in which groups or group actions are used as a main tool. The program covers many branches of modern group theory with preference given to geometric, asymptotic, and combinatorial group theory, dynamics of group actions, probabilistic and analytic methods, first-order rigidity, first-order classification, and Diophantine problems in groups and rings. More information can be found at
https://web.stevens.edu/algebraic/Stevens2024/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2406732","Conference: Southern California Geometric Analysis Seminar","DMS","GEOMETRIC ANALYSIS","04/15/2024","04/05/2024","Lei Ni","CA","University of California-San Diego","Standard Grant","Swatee Naik","03/31/2025","$29,083.00","Luca Spolaor","lni@math.ucsd.edu","9500 GILMAN DR","LA JOLLA","CA","920930021","8585344896","MPS","126500","7556","$0.00","This award provides support for the 29th Southern California Geometric Analysis Seminar to take place during the period 04/13-14, 2024 at UC San Diego. Geometric analysis is an important and growing field in modern mathematics - connecting the tools of analysis to the structures and frameworks of geometry. It is a discipline with links to many other branches of mathematics and physics. The goal of this seminar is to disseminate recent progress in geometric analysis to the Ph.D. students, postdoctoral researchers and mathematicians in the Southern California Area and beyond. Organizers plan on a broad and diverse recruitment.

Geometric analysts have combined the powerful tools of analysis with the foundations of geometry to solve a large number of problems across wide-ranging fields of study. These include global geometry, algebraic geometry, topology, several complex variables and fields within physics such as general relativity and string theory. This event will feature seven internationally known, invited speakers. More information is found at the conference website at https://mathweb.ucsd.edu/~scgas/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405266","RUI: Quotient Spaces and the Double Soul Conjecture","DMS","GEOMETRIC ANALYSIS","07/01/2024","06/07/2024","Jason DeVito","TN","University of Tennessee Martin","Standard Grant","Qun Li","06/30/2027","$136,007.00","","jdevito@utm.edu","304 ADMINISTRATION BLDG","MARTIN","TN","382380001","7318817015","MPS","126500","","$0.00","The Principal Investigator will investigate shapes called manifolds which are of particular importance due to the critical role they play in Einstein's general theory of relativity. His main focus will be on a special class of manifolds which are called double disk bundles. The PI intends to increase our understanding of the relationships which exist between double disk bundles and other important classes of manifolds. The PI will accomplish this via projects ranging in scope from undergraduate research experiences to international collaborations.

The PI's work, motivated by the Double Soul Conjecture and the recent introduction of codimension one biquotient foliations, seeks to improve our understanding of double disk bundles both topologically and geometrically. From the topological side, he intends to increase our understanding of when certain spaces of geometric interest, such as homogeneous spaces and biquotients, carry a double disk bundle structure. On the geometric side, he intends to use double disk bundle structures in the construction of new examples of manifolds with interesting Riemannian metrics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2405440","Rigidity and Flexibility through Group Actions","DMS","GEOMETRIC ANALYSIS","07/01/2024","06/03/2024","Kurt Vinhage","UT","University of Utah","Standard Grant","Eriko Hironaka","06/30/2027","$207,485.00","","vinhage@math.utah.edu","201 PRESIDENTS CIR","SALT LAKE CITY","UT","841129049","8015816903","MPS","126500","","$0.00","A traditional dynamical system is a time lapse of a space that describes the motion of points. The time lapse can be in a single, discrete time step or a continuous time flow. One natural way in which dynamical systems can be considered the same, called conjugacy, is through change of coordinates. That is, two dynamical systems are conjugate if there is an equivalence between the spaces which connects the way in which time steps are made. One of the central classification questions in dynamics is to classify dynamical systems up to conjugacy. This question has variations based on what it means for two systems to be equivalent, usually taking the forms of measurable, continuous and smooth equivalences. The goal of the proposal is to study the classification question from various perspectives, including generalizing the notion of a dynamical system to a group action, understanding possible values for conjugacy invariants and relaxing the notion of conjugacy to allow for time reparameterization. The proposal also includes work with students at various levels to deepen the collective understanding.

The proposal aims to capitalize on momentum in 3 key areas: smooth rigidity for actions of abelian groups and higher-rank semisimple Lie groups, Kakutani equivalence for flows and group actions, and flexibility for conjugacy invariants. Each of these questions is related to a classification question, the first working toward the Katok-Spatzier conjecture and Zimmer program, the second being an extension of results about Kakutani equivalence of parabolic flows to the setting of abelian group actions, and the third being a natural extension of the seminal work of Erchonko-Katok describing the possible values for topological and metric entropy for geodesic flows on surfaces.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2411029","Curvature, Metric Geometry and Topology","DMS","GEOMETRIC ANALYSIS","07/01/2024","06/03/2024","Krishnan Shankar","VA","James Madison University","Standard Grant","Qun Li","06/30/2027","$142,565.00","","shankakx@jmu.edu","800 S MAIN ST","HARRISONBURG","VA","228013104","5405686872","MPS","126500","","$0.00","The PI?s focus is the study of objects in dimensions higher than three that admit positive or non-negative curvature. Intuitively one may think of positive curvature in the following manner: On the surface of Earth any two longitudes from the North pole appear to bend towards each other and indeed they meet at the South pole. This is true of all points on Earth if we imagine longitudes emanating from each point. Because of this, we say that the surface of Earth has positive curvature everywhere. By the same token, a saddle has negative curvature at the point where the rider sits while a flat table has zero curvature. In higher dimensions, matters are far less visually apparent. One deals almost exclusively with equations and sophisticated geometrical techniques that describe the curvature of manifolds, a term that refers to objects that, roughly speaking, have no sharp edges. Manifolds of bounded size are called compact manifolds. One of the great mysteries in the study of positive or non-negative curvature is the dearth of examples. The techniques at hand are few and the number of known examples remains relatively small. In this project the PI aims to study positively and non-negatively curved manifolds with proposed new methods of construction. The project also presents several broader impact activities including outreach, inclusivity, and undergraduate research.


The study of manifolds with positive or non-negative sectional curvature has a long history with roots as far back as Felix Klein in the late nineteenth century. The PI's work for many years has been to try and construct new examples while attempting to prove rigidity theorems in the presence of additional hypotheses. Complete manifolds of non-negative sectional curvature fall into two broad categories: compact and non-compact. In the non-compact case we have the beautiful Soul theorem of Cheeger and Gromoll: A complete, non-compact manifold with non-negative sectional curvature is diffeomorphic to a vector bundle over a closed, totally convex submanifold. In the compact case, Gromov's theorem restricts the topology sharply: The total Betti number is bounded by a constant depending only on the dimension. Beyond these theorems the question remains: which closed manifolds admit metrics of non-negative sectional curvature? In this project the PI continues their recently successful research program on constructing new manifolds with non-negative curvature as well as a new proposed method for constructing positive curvature.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2405440","Rigidity and Flexibility through Group Actions","DMS","GEOMETRIC ANALYSIS","07/01/2024","06/03/2024","Kurt Vinhage","UT","University of Utah","Standard Grant","Eriko Hironaka","06/30/2027","$207,485.00","","vinhage@math.utah.edu","201 PRESIDENTS CIR","SALT LAKE CITY","UT","841129049","8015816903","MPS","126500","","$0.00","A traditional dynamical system is a time lapse of a space that describes the motion of points. The time lapse can be in a single, discrete time step or a continuous time flow. One natural way in which dynamical systems can be considered the same, called conjugacy, is through change of coordinates. That is, two dynamical systems are conjugate if there is an equivalence between the spaces which connects the way in which time steps are made. One of the central classification questions in dynamics is to classify dynamical systems up to conjugacy. This question has variations based on what it means for two systems to be equivalent, usually taking the forms of measurable, continuous and smooth equivalences. The goal of the proposal is to study the classification question from various perspectives, including generalizing the notion of a dynamical system to a group action, understanding possible values for conjugacy invariants and relaxing the notion of conjugacy to allow for time reparameterization. The proposal also includes work with students at various levels to deepen the collective understanding.

The proposal aims to capitalize on momentum in 3 key areas: smooth rigidity for actions of abelian groups and higher-rank semisimple Lie groups, Kakutani equivalence for flows and group actions, and flexibility for conjugacy invariants. Each of these questions is related to a classification question, the first working toward the Katok-Spatzier conjecture and Zimmer program, the second being an extension of results about Kakutani equivalence of parabolic flows to the setting of abelian group actions, and the third being a natural extension of the seminal work of Erchonko-Katok describing the possible values for topological and metric entropy for geodesic flows on surfaces.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2404529","Semi-global Kuranishi Structures in Symplectic Field Theory","DMS","GEOMETRIC ANALYSIS","07/01/2024","05/22/2024","Erkao Bao","MN","University of Minnesota-Twin Cities","Continuing Grant","Swatee Naik","06/30/2027","$110,904.00","","bao@umn.edu","200 OAK ST SE","MINNEAPOLIS","MN","554552009","6126245599","MPS","126500","9251","$0.00","Contact manifolds are a special type of space that naturally emerges in various contexts. For instance, they are used to describe the orbital paths of satellites. Taking the satellite scenario, for example, a natural question to ask is whether there are recurring orbits that a satellite can traverse. Contact homology offers a systematic way to explore the geometric features of these contact manifolds. In the satellite scenario, one can gain deep insights into all possible orbital paths of satellites by analyzing recurring satellite orbits. Contact homology has been highly successful in distinguishing different contact manifolds. This project aims to refine our understanding of contact manifolds using an enhanced approach based on contact homology. Furthermore, the PI intends to apply the techniques developed in this process to study other types of spaces beyond contact manifolds, such as spaces with symmetries. Symmetries play a crucial role in many aspects of daily life. For instance, ensuring that machine learning models treat people fairly, irrespective of their gender or race, reflects a key symmetry requirement. To address these issues, the PI will conduct an REU (Research Experience for Undergraduates) program focused on developing symmetrical neural networks to mitigate gender and racial biases.

Symplectic Field Theory, introduced two decades ago, aims to provide invariants for symplectic and contact manifolds. It encompasses essential concepts such as cylindrical contact homology, contact homology, chain homotopy types of contact differential graded algebras (dga), and linearized contact homology. The projects presented here revolve around the foundational aspects of Symplectic Field Theory. The primary challenge addressed by the Principal Investigator (PI) concerns achieving transversality while preserving symmetries to derive the desired algebraic formula. Various tools and techniques, including obstruction bundle gluing and evaluation maps for cylindrical contact homology, and semi-global Kuranishi structures for contact homology, have been introduced or employed by the PI. The project applies these tools to investigate two specific invariants: the chain homotopy type of contact dga and linearized contact homology. Furthermore, the PI has developed a new tool, the semi-global Kuranishi structure for clean intersections, which lies between obstruction bundle gluing and semi-global Kuranishi structures. This tool offers increased computational efficiency and bridges seemingly unrelated techniques. The project also aims to establish a Smith-type rank inequality related to the Floer homology of the fixed point set, contributing to the understanding of the L-space conjecture.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350423","Conference: Moving to higher rank: from hyperbolic to Anosov","DMS","GEOMETRIC ANALYSIS","07/01/2024","01/30/2024","Ilesanmi Adeboye","CT","Wesleyan University","Standard Grant","Eriko Hironaka","06/30/2025","$40,000.00","Sara Maloni","iadeboye@wesleyan.edu","237 HIGH ST","MIDDLETOWN","CT","064593208","8606853683","MPS","126500","7556","$0.00","This award supports participation of US based mathematicians in the conference entitled ""Moving to higher rank: from hyperbolic to Anosov,"" which will take place in Centraro, Italy, from July 15- 19, 2024. The conference will bring together researchers and students from the classical field of hyperbolic geometry and the more recent area of higher Teichmuller theory to explore and further develop the rich connection between them. The conference will facilitate the exchange of ideas, and promote collaboration between experts in both fields, while reinforcing cooperation between the US and European mathematical communities. The organizing committee will encourage and support broad and diverse participation, and the training of the new generation of researchers.

In recent decades, the areas of hyperbolic geometry and Higher Teichmuller theory have undergone a dynamic convergence of concepts, attracting numerous scholars from hyperbolic geometry who have shifted their focus toward higher rank phenomena. Concurrently, a new generation of researchers has emerged, working at the juncture of these two domains. The conference will focus on how phenomena from hyperbolic geometry generalize to higher Teichmuller theory. Past success along these lines includes generalizations of Fenchel-Nielssen coordinates, Weil- Petersson geometry, Collar Lemmas, Length rigidity, and Patterson-Sullivan Theory. The conference will feature 18 research talks, and two lightening talk sessions for junior researchers. The URL for the conference website is https://tinyurl.com/hyp2anosov.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2404599","Geometric Analysis and Complex Geometry","DMS","GEOMETRIC ANALYSIS","06/01/2024","05/15/2024","Valentino Tosatti","NY","New York University","Standard Grant","Qun Li","05/31/2027","$339,999.00","","tosatti@post.harvard.edu","70 WASHINGTON SQ S","NEW YORK","NY","100121019","2129982121","MPS","126500","","$0.00","The principal investigator's research is concerned with the study of geometric structures on a class of spaces known as complex manifolds, which are higher-dimensional curved spaces which can be defined using complex numbers. Complex manifolds are ubiquitous objects in mathematics, and have wide-ranging applications in physics and engineering. A notable class of complex manifolds is known as Calabi-Yau manifolds, which are a fundamental tool in theoretical high-energy physics, and one of the PI's main lines of research will enhance our understanding of these manifolds and their properties. Another major direction of research revolves around the study of an evolution equation for geometric spaces known as Ricci flow, which evolves a given shape in a continuous fashion aiming to make it as round as possible. In this process, singularities may develop, and understanding their nature is a central problem in the field. This project will investigate the nature of singularities that form as time goes to infinity, in the case when the geometric evolution exists for all positive time. For broader impacts, the PI will continue mentoring and advising graduate students and postdoctoral researchers, co-organize weekly seminars, organize conferences, workshops and summer schools, and disseminate their work at conferences, meetings, and seminars, as well as via scientific publications.

The PI will use techniques from geometric analysis, nonlinear partial differential equations and holomorphic dynamics to investigate fundamental questions about the geometry of complex manifolds and symplectic 4-manifolds. The first project aims to obtain a rather complete picture of the long-time behavior of immortal solutions of Ricci flow on compact Kahler manifolds. The main difficulty is that in the cases which are not already understood, the evolving metrics are volume-collapsed as time approaches infinity, and the expected limiting space is lower-dimensional. The second project is about understanding (1,1) cohomology classes on the boundary of the Kahler cone of a Calabi-Yau manifold, and the singularities of the closed positive currents that these classes contain. The third project will attack a conjecture of Donaldson program which aims to to extend Yau's solution of the Calabi Conjecture in Kahler geometry to symplectic 4-manifolds, and explore its applications in symplectic topology.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -44,8 +45,8 @@ "2405393","Evolution Equations In Geometry","DMS","GEOMETRIC ANALYSIS","06/01/2024","05/13/2024","Tobias Colding","MA","Massachusetts Institute of Technology","Continuing Grant","Qun Li","05/31/2027","$129,353.00","","Colding@math.mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","126500","","$0.00","Evolution equations are basic objects in the sciences, describing how natural phenomena change over time. For instance, modeling of a wide class of physical phenomena, such as crystal growth and flame propagation, leads to tracking fronts moving with curvature-dependent speed. Other natural evolutions leads to other equations, many of parabolic type, e.g. Ricci flow, and many have common features. Broader impacts of the project are through mentoring graduate students and young researchers, organizing seminars, and the writing of textbooks and expository articles.

The bulk of this project concerns evolution equations. Mean curvature flow, as well as new methods for dealing with the diffeomorphism group for non compact spaces with applications to Ricci flow, will be major topics investigated. Other natural evolution equations coming from various branches of sciences will be studied as well as part of the project.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2404882","Homological Mirror Symmetry and Fukaya Categories from a Toric Perspective","DMS","GEOMETRIC ANALYSIS, EPSCoR Co-Funding","06/01/2024","05/14/2024","Andrew Hanlon","NH","Dartmouth College","Standard Grant","Eriko Hironaka","05/31/2027","$111,345.00","","andrew.d.hanlon@dartmouth.edu","7 LEBANON ST","HANOVER","NH","037552170","6036463007","MPS","126500, 915000","9150","$0.00","Interesting and impactful mathematics often arises when new connections are made between different fields of math. While even heuristic connections can be fruitful, mirror symmetry provides a fascinating direct connection, originating from modern physics, between algebraic geometry and symplectic topology that has led to major advances in both areas. Algebraic geometry is a rich and classical field of mathematics that explores shapes called algebraic varieties described by polynomial equations. Symplectic topology is a younger area that studies shapes built from a geometric formalism for classical mechanics by packaging solutions to certain partial differential equations into algebraic invariants. This project aims to deepen our understanding of the mirror symmetry phenomenon by building on new insights in a special case where the algebraic varieties are particularly symmetric. This will be done with the aim of verifying new cases of the homological mirror symmetry conjecture, exploring structural aspects of a symplectic invariant known as the Fukaya category, and investigating arithmetic aspects of mirror symmetry. The project will also involve undergraduate research projects on combinatorial problems coming from mirror symmetry.

The first technical goal of the project is to further develop functorial aspects of the toric homological mirror symmetry equivalence by enlarging the list of sheaves and functors that can be provably described in terms of Lagrangian submanifolds and geometric operations on them. These geometric functors will give a better understanding of homological mirror symmetry for singular varieties obtained by gluing toric varieties along toric strata, which can then be deformed to obtain new cases of the homological mirror symmetry conjecture. In the other direction, the project will seek to leverage the geometric flexibility of the Fukaya category to construct new group actions on derived categories of toric varieties. The project will also aim to determine when symplectic fibrations can be described in terms of cornered Liouville sectors resulting in a gluing formula for their Fukaya categories. Finally, the project will explore the extent to which the toric Frobenius morphism and its simple geometric description on the mirror can be extended to other classes of varieties with an eye towards generation time in the derived category.

This project is jointly funded by Topology and Geometric Analysis program and the Established Program to Stimulate Competitive Research (EPSCoR).

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405175","Minimal Surfaces, Groups and Geometrization","DMS","GEOMETRIC ANALYSIS","11/01/2024","05/03/2024","Antoine Song","CA","California Institute of Technology","Continuing Grant","Qun Li","10/31/2027","$121,081.00","","aysong@caltech.edu","1200 E CALIFORNIA BLVD","PASADENA","CA","911250001","6263956219","MPS","126500","","$0.00","Differential geometry is a field which studies the shape of objects. Of particular importance are shapes that are ""optimal"" under natural constraints. An important class of optimal shapes is given by ""minimal surfaces"": a soap film spanning a metal wire, which tends to minimize its energy, is an example of minimal surface. This type of surfaces appears in many places in physics, but is also of intrinsic interest. The investigator will work on deforming smooth spaces, also called ""manifolds"", into an optimal shape by using the concept of minimal surfaces. Manifolds are ubiquitous in mathematics, and hopefully this approach will give new insights on their possible shapes. This project will moreover support student training and inclusion through seminars, workshops and knowledge dissemination efforts.


The notion of ""geometric structure"" serves as a unifying concept in geometry and topology, as exemplified by the Uniformization theorem for surfaces and the Geometrization theorem for 3-manifolds. In those classical instances, geometric structures are essentially defined as homogenous spaces with a geometric discrete group action. In higher dimensions, those geometric structures are very rare, and perhaps too rigid compared to the diversity of closed manifolds. In this project, the investigator proposes to consider a more general and flexible notion: minimal surfaces in (possibly infinite dimensional) homogeneous spaces, invariant under a geometric discrete group action. With this point of view, the investigator will explore a series of questions which relates minimal surfaces to geometric group theory and representation theory. A typical problem is the following: what group can act geometrically on a connected minimal surface in a Hilbert sphere?

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2404309","Rigidity Properties in Dynamics and Geometry","DMS","GEOMETRIC ANALYSIS","06/01/2024","05/01/2024","Ralf Spatzier","MI","Regents of the University of Michigan - Ann Arbor","Continuing Grant","Eriko Hironaka","05/31/2027","$204,000.00","","spatzier@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","126500","","$0.00","Dynamical systems and ergodic theory investigate the evolution of physical, biological or mathematical systems over time, such as turbulence in a fluid flow, the motions in planetary systems or the evolution of diseases. Fundamental ideas and concepts such as information, entropy, chaos and fractals have had a profound impact on our understanding of the world. Dynamical systems and ergodic theory have developed superb tools with applications to sciences and engineering. Symbolic dynamics, for example, has been instrumental in developing efficient and safe codes for computer science. Tools and ideas from smooth dynamics are used as far afield as cell biology and meteorology. Geometry is a highly developed, ancient yet superbly active field in mathematics. It studies curves, surfaces and their higher dimensional analogs, their shapes, shortest paths, and maps between such spaces. Surveying the land for his principality, Gauss developed the fundamental notions of geodesics and curvature, laying the groundwork for modern differential geometry. It has close links with physics and applied areas like computer vision or the more current geometric and topological data analysis. Geometry and dynamics are closely connected. Indeed, important dynamical systems such as the geodesic flow come from geometry, and conversely one can use geometric tools to study dynamics. One main goal of this project is to study symmetries of dynamical systems, especially when one system is unaffected by the changes brought on by the other. The quest is to study these systems via unexpected symmetries. Important examples arise from geometry when the space contains many flat subspaces. Under additional assumptions, one can classify such spaces. Finally, group theory is introduced in both dynamics and geometry via the group of symmetries of a geometry or dynamical system. The principal investigator will continue training a new generation of researchers in mathematics, and students at all levels in their mathematical endeavors. This project includes support for research training opportunities for graduate students and summer research experiences for undergraduates.

This project will investigate rigidity phenomena in geometry and dynamics, especially actions of higher rank abelian and semi-simple Lie groups and their lattices. The latter is part of the Zimmer program. Particular emphasis will be put on hyperbolic actions of such groups. As higher-rank semisimple Lie groups and their lattices contain higher-rank abelian groups, the classification and rigidity problems for the abelian and semi-simple cases are closely related, with abundant cross-fertilization. The goal is the classification of such actions. Closely related are the study of automorphism groups of geometric structures. A further goal is to understand topological joinings of lattice actions on Furstenberg boundaries and the related problem of classifying discrete subgroups in semisimple ie groups with higher Prasad-Rapinchuk rank. Investigations in geometry will address higher-rank Riemannian manifolds and their classification, introducing novel methods. The dynamics of geodesic and frame flows will also be studied, with investigations of discrete subgroups of Lie groups for rank rigidity and measure properties. Besides establishing new results, the principal investigator also strives to find and introduce novel methods for investigating these problems which will lend themselves to applications in other areas.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405361","Variational Problems In The Theory of Minimal Surfaces","DMS","GEOMETRIC ANALYSIS","06/01/2024","05/02/2024","Giada Franz","MA","Massachusetts Institute of Technology","Standard Grant","Qun Li","05/31/2027","$194,991.00","","gfranz@mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","126500","","$0.00","A submanifold is called minimal if it is a critical point of the area functional. Minimal submanifolds are of central importance in differential geometry and arise naturally in mathematical physics, as soap films and black hole horizons, for example. Therefore, understanding their behavior is of great interest from the mathematical point of view but also for applications. The objective of this project is to take steps towards a full description of all minimal submanifolds in a given ambient manifold, inspired by the variational nature of these objects. The investigator will also conduct educational activities and practice community building, with particular attention to students and junior researchers.

The project consists of three interwoven research lines. The first seeks new insights into the topological and analytical properties of minimal surfaces obtained via min-max constructions. The second line focuses on minimal surfaces with free boundary in the three-dimensional ball, with a focus on existence theorems and global properties. Finally, the project will investigate rigidity results for minimal submanifolds of higher codimension in ambient manifolds with positive curvature.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2404309","Rigidity Properties in Dynamics and Geometry","DMS","GEOMETRIC ANALYSIS","06/01/2024","05/01/2024","Ralf Spatzier","MI","Regents of the University of Michigan - Ann Arbor","Continuing Grant","Eriko Hironaka","05/31/2027","$204,000.00","","spatzier@umich.edu","1109 GEDDES AVE, SUITE 3300","ANN ARBOR","MI","481091079","7347636438","MPS","126500","","$0.00","Dynamical systems and ergodic theory investigate the evolution of physical, biological or mathematical systems over time, such as turbulence in a fluid flow, the motions in planetary systems or the evolution of diseases. Fundamental ideas and concepts such as information, entropy, chaos and fractals have had a profound impact on our understanding of the world. Dynamical systems and ergodic theory have developed superb tools with applications to sciences and engineering. Symbolic dynamics, for example, has been instrumental in developing efficient and safe codes for computer science. Tools and ideas from smooth dynamics are used as far afield as cell biology and meteorology. Geometry is a highly developed, ancient yet superbly active field in mathematics. It studies curves, surfaces and their higher dimensional analogs, their shapes, shortest paths, and maps between such spaces. Surveying the land for his principality, Gauss developed the fundamental notions of geodesics and curvature, laying the groundwork for modern differential geometry. It has close links with physics and applied areas like computer vision or the more current geometric and topological data analysis. Geometry and dynamics are closely connected. Indeed, important dynamical systems such as the geodesic flow come from geometry, and conversely one can use geometric tools to study dynamics. One main goal of this project is to study symmetries of dynamical systems, especially when one system is unaffected by the changes brought on by the other. The quest is to study these systems via unexpected symmetries. Important examples arise from geometry when the space contains many flat subspaces. Under additional assumptions, one can classify such spaces. Finally, group theory is introduced in both dynamics and geometry via the group of symmetries of a geometry or dynamical system. The principal investigator will continue training a new generation of researchers in mathematics, and students at all levels in their mathematical endeavors. This project includes support for research training opportunities for graduate students and summer research experiences for undergraduates.

This project will investigate rigidity phenomena in geometry and dynamics, especially actions of higher rank abelian and semi-simple Lie groups and their lattices. The latter is part of the Zimmer program. Particular emphasis will be put on hyperbolic actions of such groups. As higher-rank semisimple Lie groups and their lattices contain higher-rank abelian groups, the classification and rigidity problems for the abelian and semi-simple cases are closely related, with abundant cross-fertilization. The goal is the classification of such actions. Closely related are the study of automorphism groups of geometric structures. A further goal is to understand topological joinings of lattice actions on Furstenberg boundaries and the related problem of classifying discrete subgroups in semisimple ie groups with higher Prasad-Rapinchuk rank. Investigations in geometry will address higher-rank Riemannian manifolds and their classification, introducing novel methods. The dynamics of geodesic and frame flows will also be studied, with investigations of discrete subgroups of Lie groups for rank rigidity and measure properties. Besides establishing new results, the principal investigator also strives to find and introduce novel methods for investigating these problems which will lend themselves to applications in other areas.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2404992","Minimal Surfaces and Harmonic Maps in Differential Geometry","DMS","GEOMETRIC ANALYSIS","07/01/2024","05/02/2024","Daniel Stern","NY","Cornell University","Continuing Grant","Qun Li","06/30/2027","$76,032.00","","daniel.stern@cornell.edu","341 PINE TREE RD","ITHACA","NY","148502820","6072555014","MPS","126500","","$0.00","Solutions of geometric variational problems--objects which (locally) minimize natural notions of energy--play a central role in modern geometry and analysis, as well as physics, materials science, and engineering, where they characterize equilibrium states for various systems. Among the most important examples are harmonic maps, which arise in computer graphics and the study of liquid crystals, and minimal surfaces, which model soap films and the boundaries of black holes. The central goal of this project is to advance our understanding of the existence and structure of these objects, with an emphasis on connections to spectral geometry and certain geometric equations arising in particle physics. This project also involves the training of graduate students and postdocs, the organization of seminars and workshops on related topics, and dissemination of ideas to non-expert audiences through public lectures and survey articles.

This project concerns the existence and geometric structure of harmonic maps, minimal surfaces and minimal submanifolds of codimension 2 and 3, in relation to isoperimetric problems in spectral geometry and singularity formation for gauge-theoretic PDEs. With his collaborators, the PI will exploit new techniques for constructing extremal metrics for Laplacian and Steklov eigenvalues--developed in recent work of the PI with Karpukhin, Kusner, and McGrath--to produce many new minimal surfaces of prescribed topology in low-dimensional spheres and balls, and study related constructions of minimal surfaces in generic ambient spaces via mapping methods. Building on prior work with Pigati and Parise-Pigati, the PI will continue to investigate the relationship between the abelian Higgs model and minimal submanifolds of codimension two, and explore an analogous correspondence between the SU(2)-Yang-Mills-Higgs equations and minimal varieties of codimension 3. In another direction, the PI will further develop the existence and regularity theory for harmonic maps on manifolds of supercritical dimension n ? 3, combining variational methods with new analytic techniques to study the existence and compactness theory for harmonic maps with bounded Morse index into general targets.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2403728","Singularity, Rigidity, and Extremality Phenomena in Minimal Hypersurfaces","DMS","GEOMETRIC ANALYSIS","06/01/2024","05/01/2024","Christos Mantoulidis","TX","William Marsh Rice University","Standard Grant","Qun Li","05/31/2027","$215,057.00","","christos.mantoulidis@rice.edu","6100 MAIN ST","Houston","TX","770051827","7133484820","MPS","126500","","$0.00","Riemannian geometry is a modern version of geometry that studies shapes in any number of dimensions. Other than ""lengths"" and ""angles,"" its key notions also include ""minimal surfaces,"" which generalize the concept of a straight line, and ""curvature,"" which measures how a shape is bent. The principal investigator (PI) will study problems involving minimal surfaces and their curvature that arise from physical theories including Einstein?s general theory of relativity and the van der Waals?Cahn?Hilliard theory for phase transitions in multicomponent alloy systems. In addition to the research, this project will also support the PI's continued efforts to promote student learning and training through seminar organization, conferences, expository articles, and notes.

This project will specifically examine singularity, rigidity, and extremality phenomena in the theory of minimal surfaces. First, the PI will further investigate the structure of minimal surface singularities, meaning points of curvature blow-up, in area-minimization problems as well as their dynamic counterpart in mean curvature flow. Second, the PI will study enhanced rigidity properties of critical points in the van der Waals?Cahn?Hilliard phase transition theory, which can be thought of as diffuse variants of minimal surfaces. Third, the PI will study extremal behaviors of different quasi-local mass notions in general relativity, as seen through their interactions with scalar curvature and minimal surfaces, which correspond to energy density and boundaries of black hole regions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2426238","Conference: Pacific Northwest Geometry Seminar","DMS","GEOMETRIC ANALYSIS","06/01/2024","04/26/2024","Christine Escher","OR","Oregon State University","Standard Grant","Eriko Hironaka","05/31/2027","$50,397.00","Tracy Payne, Eric Bahuaud","tine@math.orst.edu","1500 SW JEFFERSON AVE","CORVALLIS","OR","973318655","5417374933","MPS","126500","7556","$0.00","This award will support meetings of the Pacific Northwest Geometry Seminar (PNGS) to be held at the University of British Columbia (2025), Seattle University (2026) and Lewis & Clark College (2027). Active researchers in geometry are scattered throughout the various colleges and universities involved in the Pacific Northwest Geometry Seminar. The PNGS meetings will bring these researchers together for consultation, collaboration, and stimulation of new ideas, and will give graduate students an excellent opportunity to see the broader picture of research in geometry. The meetings are also valuable for the growing number of geometers working at some of the smaller universities in the region, such as Pacific University, Seattle University, and Idaho State University. Conference support will be especially targeted toward graduate students, early career researchers and members of groups underrepresented in mathematics.

The meetings will feature five to six invited research talks by leading experts in differential geometry and geometric analysis, as well as three to four shorter talks by junior researchers or graduate students. The meetings will also include discussion sessions in which the speakers and participants assess the state of various areas in geometry and highlight open problems in these areas. For the first meeting at the University of British Columbia the grant will support travel of US based participants only. More information can be found on the conference website: https://sites.google.com/view/pnwgeometryseminar/home.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." diff --git a/Mathematical-Biology/Awards-Mathematical-Biology-2024.csv b/Mathematical-Biology/Awards-Mathematical-Biology-2024.csv index 456997b..0ce0ba2 100644 --- a/Mathematical-Biology/Awards-Mathematical-Biology-2024.csv +++ b/Mathematical-Biology/Awards-Mathematical-Biology-2024.csv @@ -1,33 +1,41 @@ "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract" +"2421260","Collaborative Research: IHBEM: Beneath the Surface: Integrating Wastewater Surveillance and Human Behavior to Decode Epidemiological Patterns","DMS","MATHEMATICAL BIOLOGY, MSPA-INTERDISCIPLINARY","09/01/2024","08/20/2024","Bruce Pell","MI","Lawrence Technological University","Standard Grant","Zhilan Feng","08/31/2027","$110,374.00","","bpell@ltu.edu","21000 W 10 MILE RD","SOUTHFIELD","MI","480751051","2482042103","MPS","733400, 745400","9178, 9179","$0.00","How can disease outbreaks in an increasingly interconnected world be better predicted and responded to? The project tackles this challenge by combining two key sources of information: community wastewater and human behaviors. While current methods often rely on delayed and inaccurate medical reports, our innovative approach analyzes traces of viruses in sewage and incorporates various types of data about human activity. This includes information on people's movements, social interactions, online searches, social media posts, and immune factors. By combining these diverse data sources, the Investigators aim to detect diseases earlier and gain a more comprehensive understanding of how they spread through communities. The investigators will also examine how public attitudes and behaviors evolve during prolonged health crises. Although the initial focus is on COVID-19, the methods to be developed could be applied to other infectious diseases, helping communities worldwide prepare for future health emergencies. Beyond the research, the investigators are committed to training undergraduate and graduate students from diverse backgrounds, nurturing the next generation of public health professionals. Ultimately, this project will provide valuable tools for health officials to make quicker, more informed decisions to protect public health.

The goal of this project is to enhance mathematical epidemiological modeling by integrating human behavioral data with wastewater surveillance data, creating a more comprehensive and timely approach to outbreak detection and response. By synthesizing advancements across mathematical modeling, wastewater epidemiology, and geographic information science (GIScience), the research approach innovatively connects human behavior insights with wastewater data to enhance viral transmission understanding and forecasts at the community level. To achieve this, the Investigators will pursue three main objectives: (1) Develop an early-warning system using wastewater and digital and social behavior data; (2) Create a socio-immuno-epidemiological framework to examine the effectiveness of pharmaceutical interventions and the emergence of dominant variants using wastewater surveillance data; and (3) Model the impact of pandemic fatigue social behaviors on viral transmission at the community level. These objectives will be addressed by a interdisciplinary research team, which brings together expertise in applied mathematics, epidemiology, public health, and geography. This approach represents a significant step forward in understanding the complex interactions between human behavior, immune responses, and pathogen spread. Ultimately, the research outcomes will equip health officials with valuable tools for designing proactive, targeted, and adaptable interventions, enabling quicker and more informed decision-making. This award is co-funded by DMS (Division of Mathematical Sciences) and SBE/SES (Directorate of Social, Behavioral and Economic Sciences, Division of Social and Economic Sciences).

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2410988","Collaborative Research: RUI: The fluid dynamics of organisms filtering particles at the mesoscale","DMS","MATHEMATICAL BIOLOGY","09/01/2024","08/19/2024","W Christopher Strickland","TN","University of Tennessee Knoxville","Standard Grant","Zhilan Feng","08/31/2027","$170,164.00","","cstric12@utk.edu","201 ANDY HOLT TOWER","KNOXVILLE","TN","379960001","8659743466","MPS","733400","","$0.00","Numerous small organisms that swim, fly, smell, or feed in flows at scales in which inertial and viscous forces are nearly balanced rely on using branched, bristled, and hairy body structures. Such structures have significant biological implications. In coral, they determine the success rate of catching prey through particle capture, and there are many other organisms which similarly rely on the transition of their body structures from solid surfaces to leaky/porous ?rakes.? Active particles (e.g. swimming plankton and microorganisms) can also enhance or reduce capture through their own behaviors. Although flows around such organisms have been studied before, the fluid dynamic mechanisms underlying the leaky-rake to solid-plate transition and how it affects particle capture remain unclear. The goal of this project is the development of open-source numerical software to elucidate the fluid dynamics of such biological and bioinspired filtering arrays, including how the individual and collective behavior of the active particles affects filtering outcomes. In addition, the Investigators will design software training materials and complementary classroom modules. The Investigators will engage in public outreach for all ages through targeted modalities for different age demographics such as participating in the Skype A Scientist program for younger children and coral reef conservation courses aimed at older retirees which will incorporate math and physics.

The natural world is replete with mesoscale filters that are significant to biological and biomedical applications. These are, however, challenging multiscale problems that require high accuracy to resolve the flow through complex structures that are sensitive to small perturbations. To understand these problems, the research team aims to 1) develop a Method of Regularized Oseenlets that can be employed as a gridless method to resolve flows through filtering structures for Reynolds numbers near unity, 2) develop and test force spreading operators that are independent of the grid size for the immersed boundary method, 3) develop and implement numerical techniques to efficiently describe the interactions of agents in flow with moving, complex 3D boundaries, and 4) implement tools from sensitivity analysis and uncertainty quantification to reveal which parameters are important for particle capture and to guide the development of more detailed agent and flow models. Upon doing so, the project will focus on the filter feeding of plankton by Cnidarians and will address the following (i) identifying small-scale flow patterns within rigid and flexible filtering structures at the leaky-to-solid transition, (ii) understanding how small-scale flow patterns affect the capture of Brownian swimmers, and (iii) determining the collective effect of fundamental behaviors in small organisms for capture and targeting in the presence of flow. The frameworks developed here can be broadly applied to other biological systems where mesoscale exchange occurs, e.g. the filtering structures of fish or the chemical sensors of insects and crabs.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2410987","Collaborative Research: RUI: The fluid dynamics of organisms filtering particles at the mesoscale","DMS","MATHEMATICAL BIOLOGY","09/01/2024","08/19/2024","Nicholas Battista","NJ","The College of New Jersey","Standard Grant","Zhilan Feng","08/31/2027","$124,157.00","","battistn@tcnj.edu","2000 PENNINGTON RD","EWING","NJ","086181104","6097713255","MPS","733400","9229","$0.00","Numerous small organisms that swim, fly, smell, or feed in flows at scales in which inertial and viscous forces are nearly balanced rely on using branched, bristled, and hairy body structures. Such structures have significant biological implications. In coral, they determine the success rate of catching prey through particle capture, and there are many other organisms which similarly rely on the transition of their body structures from solid surfaces to leaky/porous ?rakes.? Active particles (e.g. swimming plankton and microorganisms) can also enhance or reduce capture through their own behaviors. Although flows around such organisms have been studied before, the fluid dynamic mechanisms underlying the leaky-rake to solid-plate transition and how it affects particle capture remain unclear. The goal of this project is the development of open-source numerical software to elucidate the fluid dynamics of such biological and bioinspired filtering arrays, including how the individual and collective behavior of the active particles affects filtering outcomes. In addition, the Investigators will design software training materials and complementary classroom modules. The Investigators will engage in public outreach for all ages through targeted modalities for different age demographics such as participating in the Skype A Scientist program for younger children and coral reef conservation courses aimed at older retirees which will incorporate math and physics.

The natural world is replete with mesoscale filters that are significant to biological and biomedical applications. These are, however, challenging multiscale problems that require high accuracy to resolve the flow through complex structures that are sensitive to small perturbations. To understand these problems, the research team aims to 1) develop a Method of Regularized Oseenlets that can be employed as a gridless method to resolve flows through filtering structures for Reynolds numbers near unity, 2) develop and test force spreading operators that are independent of the grid size for the immersed boundary method, 3) develop and implement numerical techniques to efficiently describe the interactions of agents in flow with moving, complex 3D boundaries, and 4) implement tools from sensitivity analysis and uncertainty quantification to reveal which parameters are important for particle capture and to guide the development of more detailed agent and flow models. Upon doing so, the project will focus on the filter feeding of plankton by Cnidarians and will address the following (i) identifying small-scale flow patterns within rigid and flexible filtering structures at the leaky-to-solid transition, (ii) understanding how small-scale flow patterns affect the capture of Brownian swimmers, and (iii) determining the collective effect of fundamental behaviors in small organisms for capture and targeting in the presence of flow. The frameworks developed here can be broadly applied to other biological systems where mesoscale exchange occurs, e.g. the filtering structures of fish or the chemical sensors of insects and crabs.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2424684","eMB: Multi-state bootstrap percolation on digraphs as a framework for neuronal network analysis","DMS","IIBR: Infrastructure Innovatio, MATHEMATICAL BIOLOGY","09/01/2024","08/07/2024","Jonathan Rubin","PA","University of Pittsburgh","Standard Grant","Zhilan Feng","08/31/2027","$384,792.00","Gregory Constantine, Mohammad Amin Rahimian, Sabrina Streipert","jonrubin@pitt.edu","4200 FIFTH AVENUE","PITTSBURGH","PA","152600001","4126247400","MPS","084Y00, 733400","068Z, 8038, 8091","$0.00","To study the spread of disease or opinions, it has proven useful to consider a collection of interacting individuals as a mathematical structure called a graph. A graph consists of a set of nodes and a set of edges, each of which links a pair of nodes. PI will extend this framework to the study of neuronal activity. In the neuronal case, each node is a neuron, and edges between them represent the one-way or directed synaptic connections through which neurons interact. Moreover, to capture the different levels of activity that neurons exhibit, each node will be in one of three states, with state changes determined by interactions along edges. PI will develop novel mathematical methods to analyze the patterns of activity that emerge in such multi-state, directed graphs. These methods will allow the project team to study how activity spreads in networks of neurons, how this spread depends on the connection patterns in the network, and what properties characterize sets of nodes that are especially effective at spreading activity. The research results will generate novel predictions about the properties and function of networks of neurons in the brain, with a focus on the key networks that drive breathing and other essential, rhythmic behaviors. The project will train students, will generate openly available computer code, and will include public outreach through online videos and a summer math program for girls.

Functional outputs from brain circuits driving certain critical, rhythmic behaviors require the widespread emergence of an elevated, bursting state of neuronal activity. The main goal of this project is to advance knowledge about how the localized initiation of activity can rapidly evolve into widespread bursting in synaptically coupled neuronal networks, exemplified by the respiratory brainstem circuit. The project team will achieve this goal by representing such networks as digraphs in which each node can assume one of three possible activity states ? inactive, weakly active, and fully active or bursting -- with updates based on in-neighbors? states. Little theory exists to characterize this multi-state bootstrap percolation framework, and we will develop new analytical approaches involving mean field and master equations, asymptotic and probabilistic estimates, and graph design based on combinatorial principles. The analysis will address differences between dynamics in this framework and that in bootstrap percolation with only two possible states per node, the impact of global graph properties on activity spread, and the characteristics of local initiation sites that result in especially effective activity propagation. Overall, the project will support a new interdisciplinary collaboration and the completed work, involving trainee mentorship and open sharing of code, will provide important insights and predictions about neuronal dynamics and interactions as well as a range of mathematical advances.

This project is jointly funded by the Mathematical Biology Program in the Division of Mathematical Sciences and the Research Resources Cluster in the Division of Biological Infrastructure in the Directorate for Biological Sciences.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2421258","Collaborative Research: IHBEM: Beneath the Surface: Integrating Wastewater Surveillance and Human Behavior to Decode Epidemiological Patterns","DMS","MATHEMATICAL BIOLOGY, MSPA-INTERDISCIPLINARY","09/01/2024","08/20/2024","Yang Kuang","AZ","Arizona State University","Standard Grant","Zhilan Feng","08/31/2027","$99,988.00","","kuang@asu.edu","660 S MILL AVENUE STE 204","TEMPE","AZ","852813670","4809655479","MPS","733400, 745400","9178, 9179","$0.00","How can disease outbreaks in an increasingly interconnected world be better predicted and responded to? The project tackles this challenge by combining two key sources of information: community wastewater and human behaviors. While current methods often rely on delayed and inaccurate medical reports, our innovative approach analyzes traces of viruses in sewage and incorporates various types of data about human activity. This includes information on people's movements, social interactions, online searches, social media posts, and immune factors. By combining these diverse data sources, the Investigators aim to detect diseases earlier and gain a more comprehensive understanding of how they spread through communities. The investigators will also examine how public attitudes and behaviors evolve during prolonged health crises. Although the initial focus is on COVID-19, the methods to be developed could be applied to other infectious diseases, helping communities worldwide prepare for future health emergencies. Beyond the research, the investigators are committed to training undergraduate and graduate students from diverse backgrounds, nurturing the next generation of public health professionals. Ultimately, this project will provide valuable tools for health officials to make quicker, more informed decisions to protect public health.

The goal of this project is to enhance mathematical epidemiological modeling by integrating human behavioral data with wastewater surveillance data, creating a more comprehensive and timely approach to outbreak detection and response. By synthesizing advancements across mathematical modeling, wastewater epidemiology, and geographic information science (GIScience), the research approach innovatively connects human behavior insights with wastewater data to enhance viral transmission understanding and forecasts at the community level. To achieve this, the Investigators will pursue three main objectives: (1) Develop an early-warning system using wastewater and digital and social behavior data; (2) Create a socio-immuno-epidemiological framework to examine the effectiveness of pharmaceutical interventions and the emergence of dominant variants using wastewater surveillance data; and (3) Model the impact of pandemic fatigue social behaviors on viral transmission at the community level. These objectives will be addressed by a interdisciplinary research team, which brings together expertise in applied mathematics, epidemiology, public health, and geography. This approach represents a significant step forward in understanding the complex interactions between human behavior, immune responses, and pathogen spread. Ultimately, the research outcomes will equip health officials with valuable tools for designing proactive, targeted, and adaptable interventions, enabling quicker and more informed decision-making. This award is co-funded by DMS (Division of Mathematical Sciences) and SBE/SES (Directorate of Social, Behavioral and Economic Sciences, Division of Social and Economic Sciences).

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2421257","Collaborative Research: IHBEM: Beneath the Surface: Integrating Wastewater Surveillance and Human Behavior to Decode Epidemiological Patterns","DMS","MATHEMATICAL BIOLOGY, MSPA-INTERDISCIPLINARY","09/01/2024","08/20/2024","Fuqing Wu","TX","The University of Texas Health Science Center at Houston","Standard Grant","Zhilan Feng","08/31/2027","$315,507.00","Catherine Troisi","fuqing.wu@uth.tmc.edu","7000 FANNIN ST FL 9","HOUSTON","TX","770303870","7135003999","MPS","733400, 745400","9178, 9179","$0.00","How can disease outbreaks in an increasingly interconnected world be better predicted and responded to? The project tackles this challenge by combining two key sources of information: community wastewater and human behaviors. While current methods often rely on delayed and inaccurate medical reports, our innovative approach analyzes traces of viruses in sewage and incorporates various types of data about human activity. This includes information on people's movements, social interactions, online searches, social media posts, and immune factors. By combining these diverse data sources, the Investigators aim to detect diseases earlier and gain a more comprehensive understanding of how they spread through communities. The investigators will also examine how public attitudes and behaviors evolve during prolonged health crises. Although the initial focus is on COVID-19, the methods to be developed could be applied to other infectious diseases, helping communities worldwide prepare for future health emergencies. Beyond the research, the investigators are committed to training undergraduate and graduate students from diverse backgrounds, nurturing the next generation of public health professionals. Ultimately, this project will provide valuable tools for health officials to make quicker, more informed decisions to protect public health.

The goal of this project is to enhance mathematical epidemiological modeling by integrating human behavioral data with wastewater surveillance data, creating a more comprehensive and timely approach to outbreak detection and response. By synthesizing advancements across mathematical modeling, wastewater epidemiology, and geographic information science (GIScience), the research approach innovatively connects human behavior insights with wastewater data to enhance viral transmission understanding and forecasts at the community level. To achieve this, the Investigators will pursue three main objectives: (1) Develop an early-warning system using wastewater and digital and social behavior data; (2) Create a socio-immuno-epidemiological framework to examine the effectiveness of pharmaceutical interventions and the emergence of dominant variants using wastewater surveillance data; and (3) Model the impact of pandemic fatigue social behaviors on viral transmission at the community level. These objectives will be addressed by a interdisciplinary research team, which brings together expertise in applied mathematics, epidemiology, public health, and geography. This approach represents a significant step forward in understanding the complex interactions between human behavior, immune responses, and pathogen spread. Ultimately, the research outcomes will equip health officials with valuable tools for designing proactive, targeted, and adaptable interventions, enabling quicker and more informed decision-making. This award is co-funded by DMS (Division of Mathematical Sciences) and SBE/SES (Directorate of Social, Behavioral and Economic Sciences, Division of Social and Economic Sciences).

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2424635","eMB: Collaborative Research: A mathematical theory for the biological concept of modularity","DMS","MATHEMATICAL BIOLOGY","11/01/2024","08/16/2024","Reinhard Laubenbacher","FL","University of Florida","Standard Grant","Zhilan Feng","10/31/2027","$95,465.00","","reinhard.laubenbacher@medicine.ufl.edu","1523 UNION RD RM 207","GAINESVILLE","FL","326111941","3523923516","MPS","733400","068Z, 8038","$0.00","Biological phenomena are often driven by complex dynamic regulatory networks. In natural or engineered systems, complicated structures can be generated from simpler building blocks, or modules. This notion of complex systems built from modules is also prevalent in modern systems biology. However, a clear theoretical foundation of modularity, including useful definitions of basic concepts and mechanisms, is still missing. This research project will fill this gap by defining modular structures in biological systems in a mathematically rigorous way. The research will determine why modularity can be advantageous to an organism and elucidate how modularity can be leveraged to advance our understanding of molecular systems. Studying the modularity of specific gene regulatory networks underlying salamander limb regeneration as well as hormone regulation in plants harbors the potential to reveal novel biological insights. Through involvement of students in all aspects of the research, this project contributes to the interdisciplinary training of STEM workforce. The dissemination of results through a dedicated project website and webinars enables anyone to analyze biological network models.

The foundation of this project is a rigorous, structure-based definition of modularity in the context of Boolean networks, a common modeling framework in systems biology. Through computational, experimental, and theoretical studies, it will be shown that this definition of modularity (i) is biologically meaningful, (ii) implies a decomposition of the dynamics of Boolean networks, which can be employed to efficiently compute their dynamics, and (iii) that modular networks can be controlled effectively. The theoretical results, including theorems and implemented algorithms for practical computation, will advance the body of knowledge in the fields of network analysis, systems biology, and developmental biology. The validity of the project will be demonstrated through (1) in vivo analyses in the model plant Arabidopsis, (2) in silico analyses in an emerging animal model, axolotl. This will yield novel biological insights regarding (1) the interplay between phytohormones during Arabidopsis organogenesis, and (2) gene regulatory networks directing fibroblast reprogramming in axolotls.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2424634","eMB: Collaborative Research: A mathematical theory for the biological concept of modularity","DMS","MATHEMATICAL BIOLOGY","11/01/2024","08/16/2024","Alan Veliz-Cuba","OH","University of Dayton","Standard Grant","Zhilan Feng","10/31/2027","$116,354.00","","avelizcuba1@udayton.edu","300 COLLEGE PARK AVE","DAYTON","OH","454690001","9372292919","MPS","733400","068Z, 8038","$0.00","Biological phenomena are often driven by complex dynamic regulatory networks. In natural or engineered systems, complicated structures can be generated from simpler building blocks, or modules. This notion of complex systems built from modules is also prevalent in modern systems biology. However, a clear theoretical foundation of modularity, including useful definitions of basic concepts and mechanisms, is still missing. This research project will fill this gap by defining modular structures in biological systems in a mathematically rigorous way. The research will determine why modularity can be advantageous to an organism and elucidate how modularity can be leveraged to advance our understanding of molecular systems. Studying the modularity of specific gene regulatory networks underlying salamander limb regeneration as well as hormone regulation in plants harbors the potential to reveal novel biological insights. Through involvement of students in all aspects of the research, this project contributes to the interdisciplinary training of STEM workforce. The dissemination of results through a dedicated project website and webinars enables anyone to analyze biological network models.

The foundation of this project is a rigorous, structure-based definition of modularity in the context of Boolean networks, a common modeling framework in systems biology. Through computational, experimental, and theoretical studies, it will be shown that this definition of modularity (i) is biologically meaningful, (ii) implies a decomposition of the dynamics of Boolean networks, which can be employed to efficiently compute their dynamics, and (iii) that modular networks can be controlled effectively. The theoretical results, including theorems and implemented algorithms for practical computation, will advance the body of knowledge in the fields of network analysis, systems biology, and developmental biology. The validity of the project will be demonstrated through (1) in vivo analyses in the model plant Arabidopsis, (2) in silico analyses in an emerging animal model, axolotl. This will yield novel biological insights regarding (1) the interplay between phytohormones during Arabidopsis organogenesis, and (2) gene regulatory networks directing fibroblast reprogramming in axolotls.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2421289","IHBEM: No One Lives in a Bubble: Incorporating Group Dynamics into Epidemic Models","DMS","Human Networks & Data Sci Res, MATHEMATICAL BIOLOGY, MSPA-INTERDISCIPLINARY","09/01/2024","08/19/2024","Babak Heydari","MA","Northeastern University","Continuing Grant","Zhilan Feng","08/31/2027","$365,571.00","Daniel O'Brien, Gabor Lippner, Silvia Prina","b.heydari@northeastern.edu","360 HUNTINGTON AVE","BOSTON","MA","021155005","6173733004","MPS","147Y00, 733400, 745400","068Z","$0.00","The dynamics of human behavior play a crucial role in the spread of epidemics. While much research has focused on individual reactions to risks and policies, this project examines how groups of people, such as households, communities, or organizations, demonstrate coordinated risk-mitigating behavior and make collective decisions during an epidemic. These group-level behaviors can significantly impact the trajectory of an epidemic, beyond what can be captured by aggregating individual behaviors. By studying group behaviors, such as the formation of social bubbles and changes in risk-mitigating norms and conventions, this research aims to create better mathematical models that reflect real-world social interactions. These models will help scientists and policymakers develop more effective strategies for managing epidemics, ultimately saving lives and reducing social and economic impacts. Additionally, insights from this research could inform policies on a range of issues including gun violence, opioid abuse, disaster response, and community resilience, where group behaviors play a critical role.

The research concentrates on two main questions: 1) How can mathematical models and scalable computational algorithms be created to incorporate group-level behavioral responses in epidemic models? 2) How much do group-level responses significantly influence pandemic trajectories, and what are the resulting policy implications? The team plans to jointly work on several interconnected research thrusts. They will build mathematical foundations using a three-level network model and cooperative game theory to incorporate group-level behavioral responses, such as the formation and transformation of pandemic social bubbles and localized risk-mitigating norms within pandemic models. Next, they will create computational models that enable scalable and interpretable execution of these network-based approaches, developing dynamic networks using geospatial data and designing network downscaling algorithms to improve simulation efficiency. The team will use causal identification based on various natural experiments to estimate the input parameters of the models, focusing on empirically measuring perceived risk, peer effects on interaction networks, and the formation of social bubbles. Finally, they will implement and validate the model comprehensively at the county level in the US and at a more granular level in Boston neighborhoods, examining the policy implications of group-level behavioral responses. This award is co-funded by DMS (Division of Mathematical Sciences), SBE/SES (Directorate of Social, Behavioral and Economic Sciences, Division of Social and Economic Sciences), and SBE/BCS (Directorate of Social, Behavioral and Economic Sciences, Division of Behavioral and Cognitive Sciences).

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2410986","Collaborative Research: RUI: The fluid dynamics of organisms filtering particles at the mesoscale","DMS","MATHEMATICAL BIOLOGY","09/01/2024","08/19/2024","Laura Miller","AZ","University of Arizona","Standard Grant","Zhilan Feng","08/31/2027","$175,324.00","","lauram9@math.arizona.edu","845 N PARK AVE RM 538","TUCSON","AZ","85721","5206266000","MPS","733400","9229","$0.00","Numerous small organisms that swim, fly, smell, or feed in flows at scales in which inertial and viscous forces are nearly balanced rely on using branched, bristled, and hairy body structures. Such structures have significant biological implications. In coral, they determine the success rate of catching prey through particle capture, and there are many other organisms which similarly rely on the transition of their body structures from solid surfaces to leaky/porous ?rakes.? Active particles (e.g. swimming plankton and microorganisms) can also enhance or reduce capture through their own behaviors. Although flows around such organisms have been studied before, the fluid dynamic mechanisms underlying the leaky-rake to solid-plate transition and how it affects particle capture remain unclear. The goal of this project is the development of open-source numerical software to elucidate the fluid dynamics of such biological and bioinspired filtering arrays, including how the individual and collective behavior of the active particles affects filtering outcomes. In addition, the Investigators will design software training materials and complementary classroom modules. The Investigators will engage in public outreach for all ages through targeted modalities for different age demographics such as participating in the Skype A Scientist program for younger children and coral reef conservation courses aimed at older retirees which will incorporate math and physics.

The natural world is replete with mesoscale filters that are significant to biological and biomedical applications. These are, however, challenging multiscale problems that require high accuracy to resolve the flow through complex structures that are sensitive to small perturbations. To understand these problems, the research team aims to 1) develop a Method of Regularized Oseenlets that can be employed as a gridless method to resolve flows through filtering structures for Reynolds numbers near unity, 2) develop and test force spreading operators that are independent of the grid size for the immersed boundary method, 3) develop and implement numerical techniques to efficiently describe the interactions of agents in flow with moving, complex 3D boundaries, and 4) implement tools from sensitivity analysis and uncertainty quantification to reveal which parameters are important for particle capture and to guide the development of more detailed agent and flow models. Upon doing so, the project will focus on the filter feeding of plankton by Cnidarians and will address the following (i) identifying small-scale flow patterns within rigid and flexible filtering structures at the leaky-to-solid transition, (ii) understanding how small-scale flow patterns affect the capture of Brownian swimmers, and (iii) determining the collective effect of fundamental behaviors in small organisms for capture and targeting in the presence of flow. The frameworks developed here can be broadly applied to other biological systems where mesoscale exchange occurs, e.g. the filtering structures of fish or the chemical sensors of insects and crabs.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2421259","Collaborative Research: IHBEM: Beneath the Surface: Integrating Wastewater Surveillance and Human Behavior to Decode Epidemiological Patterns","DMS","MATHEMATICAL BIOLOGY, MSPA-INTERDISCIPLINARY","09/01/2024","08/20/2024","Tao Hu","OK","Oklahoma State University","Standard Grant","Zhilan Feng","08/31/2027","$114,990.00","","tao.hu@okstate.edu","401 WHITEHURST HALL","STILLWATER","OK","740781031","4057449995","MPS","733400, 745400","9150, 9178, 9179","$0.00","How can disease outbreaks in an increasingly interconnected world be better predicted and responded to? The project tackles this challenge by combining two key sources of information: community wastewater and human behaviors. While current methods often rely on delayed and inaccurate medical reports, our innovative approach analyzes traces of viruses in sewage and incorporates various types of data about human activity. This includes information on people's movements, social interactions, online searches, social media posts, and immune factors. By combining these diverse data sources, the Investigators aim to detect diseases earlier and gain a more comprehensive understanding of how they spread through communities. The investigators will also examine how public attitudes and behaviors evolve during prolonged health crises. Although the initial focus is on COVID-19, the methods to be developed could be applied to other infectious diseases, helping communities worldwide prepare for future health emergencies. Beyond the research, the investigators are committed to training undergraduate and graduate students from diverse backgrounds, nurturing the next generation of public health professionals. Ultimately, this project will provide valuable tools for health officials to make quicker, more informed decisions to protect public health.

The goal of this project is to enhance mathematical epidemiological modeling by integrating human behavioral data with wastewater surveillance data, creating a more comprehensive and timely approach to outbreak detection and response. By synthesizing advancements across mathematical modeling, wastewater epidemiology, and geographic information science (GIScience), the research approach innovatively connects human behavior insights with wastewater data to enhance viral transmission understanding and forecasts at the community level. To achieve this, the Investigators will pursue three main objectives: (1) Develop an early-warning system using wastewater and digital and social behavior data; (2) Create a socio-immuno-epidemiological framework to examine the effectiveness of pharmaceutical interventions and the emergence of dominant variants using wastewater surveillance data; and (3) Model the impact of pandemic fatigue social behaviors on viral transmission at the community level. These objectives will be addressed by a interdisciplinary research team, which brings together expertise in applied mathematics, epidemiology, public health, and geography. This approach represents a significant step forward in understanding the complex interactions between human behavior, immune responses, and pathogen spread. Ultimately, the research outcomes will equip health officials with valuable tools for designing proactive, targeted, and adaptable interventions, enabling quicker and more informed decision-making. This award is co-funded by DMS (Division of Mathematical Sciences) and SBE/SES (Directorate of Social, Behavioral and Economic Sciences, Division of Social and Economic Sciences).

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2424633","eMB: Collaborative Research: A mathematical theory for the biological concept of modularity","DMS","OFFICE OF MULTIDISCIPLINARY AC, MATHEMATICAL BIOLOGY","11/01/2024","08/16/2024","David Murrugarra","KY","University of Kentucky Research Foundation","Standard Grant","Zhilan Feng","10/31/2027","$210,720.00","","murrugarra@uky.edu","500 S LIMESTONE","LEXINGTON","KY","405260001","8592579420","MPS","125300, 733400","068Z, 8038, 9150","$0.00","Biological phenomena are often driven by complex dynamic regulatory networks. In natural or engineered systems, complicated structures can be generated from simpler building blocks, or modules. This notion of complex systems built from modules is also prevalent in modern systems biology. However, a clear theoretical foundation of modularity, including useful definitions of basic concepts and mechanisms, is still missing. This research project will fill this gap by defining modular structures in biological systems in a mathematically rigorous way. The research will determine why modularity can be advantageous to an organism and elucidate how modularity can be leveraged to advance our understanding of molecular systems. Studying the modularity of specific gene regulatory networks underlying salamander limb regeneration as well as hormone regulation in plants harbors the potential to reveal novel biological insights. Through involvement of students in all aspects of the research, this project contributes to the interdisciplinary training of STEM workforce. The dissemination of results through a dedicated project website and webinars enables anyone to analyze biological network models.

The foundation of this project is a rigorous, structure-based definition of modularity in the context of Boolean networks, a common modeling framework in systems biology. Through computational, experimental, and theoretical studies, it will be shown that this definition of modularity (i) is biologically meaningful, (ii) implies a decomposition of the dynamics of Boolean networks, which can be employed to efficiently compute their dynamics, and (iii) that modular networks can be controlled effectively. The theoretical results, including theorems and implemented algorithms for practical computation, will advance the body of knowledge in the fields of network analysis, systems biology, and developmental biology. The validity of the project will be demonstrated through (1) in vivo analyses in the model plant Arabidopsis, (2) in silico analyses in an emerging animal model, axolotl. This will yield novel biological insights regarding (1) the interplay between phytohormones during Arabidopsis organogenesis, and (2) gene regulatory networks directing fibroblast reprogramming in axolotls.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2424632","eMB: Collaborative Research: A mathematical theory for the biological concept of modularity","DMS","OFFICE OF MULTIDISCIPLINARY AC, MATHEMATICAL BIOLOGY","11/01/2024","08/16/2024","Claus Kadelka","IA","Iowa State University","Standard Grant","Zhilan Feng","10/31/2027","$245,723.00","Dior Kelley","ckadelka@iastate.edu","1350 BEARDSHEAR HALL","AMES","IA","500112103","5152945225","MPS","125300, 733400","068Z, 8038, 9150","$0.00","Biological phenomena are often driven by complex dynamic regulatory networks. In natural or engineered systems, complicated structures can be generated from simpler building blocks, or modules. This notion of complex systems built from modules is also prevalent in modern systems biology. However, a clear theoretical foundation of modularity, including useful definitions of basic concepts and mechanisms, is still missing. This research project will fill this gap by defining modular structures in biological systems in a mathematically rigorous way. The research will determine why modularity can be advantageous to an organism and elucidate how modularity can be leveraged to advance our understanding of molecular systems. Studying the modularity of specific gene regulatory networks underlying salamander limb regeneration as well as hormone regulation in plants harbors the potential to reveal novel biological insights. Through involvement of students in all aspects of the research, this project contributes to the interdisciplinary training of STEM workforce. The dissemination of results through a dedicated project website and webinars enables anyone to analyze biological network models.

The foundation of this project is a rigorous, structure-based definition of modularity in the context of Boolean networks, a common modeling framework in systems biology. Through computational, experimental, and theoretical studies, it will be shown that this definition of modularity (i) is biologically meaningful, (ii) implies a decomposition of the dynamics of Boolean networks, which can be employed to efficiently compute their dynamics, and (iii) that modular networks can be controlled effectively. The theoretical results, including theorems and implemented algorithms for practical computation, will advance the body of knowledge in the fields of network analysis, systems biology, and developmental biology. The validity of the project will be demonstrated through (1) in vivo analyses in the model plant Arabidopsis, (2) in silico analyses in an emerging animal model, axolotl. This will yield novel biological insights regarding (1) the interplay between phytohormones during Arabidopsis organogenesis, and (2) gene regulatory networks directing fibroblast reprogramming in axolotls.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2424853","eMB: Collaborative Research: Using mathematics to bridge between evolutionary dynamics in the hematopoietic systems of mice and humans: from in vivo to epidemiological scales","DMS","MATHEMATICAL BIOLOGY","10/01/2024","08/08/2024","Dominik Wodarz","CA","University of California-San Diego","Standard Grant","Amina Eladdadi","09/30/2027","$200,812.00","Natalia Komarova","dwodarz@ucsd.edu","9500 GILMAN DR","LA JOLLA","CA","920930021","8585344896","MPS","733400","8038","$0.00","This project is a collaboration between three institutions: University of California-San Diego, Xavier University of Louisiana, and University of California-Irvine. The human blood contains different cell types that are continuously produced, while older cells die. As this process continues while the organism ages, mistakes are made during cell production, generating mutant cells. These mutants can linger in the blood and become more abundant over time. They can contribute to chronic health conditions and there is a chance that they initiate cancer. It is not well understood why these mutant cells persist and expand. One problem that has held back progress is that for obvious reasons it is impossible to perform experiments with human subjects to investigate this. Mathematics combined with epidemiological data, however, offers a way around this limitation. This project develops mathematical models describing the evolution of mutant cells in the blood over time, using experimental mouse data to define the model structure. New mathematical approaches are then used to adapt this model to the human blood system, by bridging between mathematical models of mutant evolution in the blood, and the epidemiological age-incidence of mutants in the human population. There is broad public health impact, since this work can suggest ways to reduce the mutant cells in patients, which can alleviate chronic health conditions and reduce cancer risk. From the educational perspective, the PIs collaborate with Xavier University of Louisiana, an undergraduate historically black university, to foster enthusiasm in continued education and careers in STEM, and equip students with knowledge and skills to potentially continue in graduate programs at top universities, thus promoting social mobility.

As higher organisms age, tissue cells acquire mutations that can rise in frequency over time. Such clonal evolutionary processes have been documented in many human tissues and have become a major focus for understanding the biology of aging. Gaining more insights into mechanisms that drive mutant emergence in non-malignant human tissues is an important biological / public health question that needs to be addressed to define correlates of tissue aging. While experiments in mice have suggested possible drivers of mutant evolution in tissues, a central unresolved question is whether (and how) knowledge from murine models can be applied to humans. Mathematics provides a new approach to address this challenge: We propose a multiscale approach that uses mathematics to bridge between cellular dynamics of mice and humans, by utilizing epidemiological data of mutant incidence in human populations. We use ?clonal hematopoiesis of indeterminate potential? (CHIP) as a study system, where TET2 and DNMT3A mutant clones emerge in the histologically normal hematopoietic system. Based on stem cell transplantation experiments in mice, we seek to construct a predictive mathematical model of mutant evolution in mice. Using the hazard function, this in vivo model can predict the epidemiological incidence of mutants. Fitting predicted to observed mutant age-incidence data for humans will yield a parameterized and predictive model of human TET2 and DNMT3A mutant evolution. Public health impacts include a better understanding of mutant evolution in the human hematopoietic system, which may lead to evolution-based intervention strategies to reduce CHIP mutant burden.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2424302","eMB: Collaborative Research: Integrated Hybrid Mathematical Modeling for Schistosomiasis Elimination","DMS","MATHEMATICAL BIOLOGY","09/01/2024","08/13/2024","Yang Yang","GA","University of Georgia","Standard Grant","Amina Eladdadi","08/31/2027","$133,203.00","","yang.yang4@uga.edu","623 BOYD GRADUATE RESEARCH CTR","ATHENS","GA","306020001","7065425939","MPS","733400","8038, 8083","$0.00","This project is a collaboration amongst the University of Florida (Gainesville), the University of Georgia (Athens), and the University of Massachusetts (Amherst).

Schistosomiasis, a disease caused by parasitic worms and transmitted through contact with contaminated freshwater, poses a significant public health threat in many developing regions. Hence, designing effective intervention strategies to mitigate the disease?s impact is timely and critical. This project aims to advance our understanding of schistosomiasis transmission dynamics and control. Specifically focusing on schistosomiasis in Zanzibar and Ethiopia, this research will create and use innovative mathematical modeling tools to understand how various factors like human movement and environmental changes influence disease transmission. This will help to identify the best strategies to control and eventually eliminate schistosomiasis as a public health problem. The project is not only scientifically important but also has significant public health, educational, and societal implications. The educational and societal impacts include training a diverse group of students (including students from underrepresented groups) and fostering interdisciplinary and collaborative research skills. The project will provide novel analytic tools for efficient resource management and inform evidence-based policies for sustainable elimination of schistosomiasis, thereby significantly impacting global health. A workshop in Zanzibar will further help building workforce in quantitative public health and disseminating scientific knowledge.

The proposed project seeks to develop advanced mathematical models to improve our understanding and management of schistosomiasis transmission dynamics, especially during the transition from high to low transmission phases towards elimination. Current models often fail to adequately capture low transmission environments, where random events, spatial and temporal heterogeneities, as well as environmental factors significantly impact transmission persistence. The project aims to develop a novel and robust hybrid deterministic-agent-based modeling framework integrating snail population dynamics (an aspect hither to overlooked in many schistosomiases transmission models) and environmental factors, using data for Schistosoma haematobium from Zanzibar and Schistosoma mansoni from Ethiopia. This innovative dual-phase framework will capture complexities in both high and low transmission settings, incorporating human movement, hydrological networks, and parasite gene flow. The project will assess persistence drivers under low-level transmission, identify transmission breakpoints, and optimize intervention strategies, offering new insights into transmission dynamics and control strategies that lead to impactful public health policies.?

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2347200","Integrating theory and experiment to understand the effects of press and pulse disturbances on competitive and consumer-resource interactions","DMS","Population & Community Ecology, MATHEMATICAL BIOLOGY","08/15/2024","08/15/2024","Katriona Shea","PA","Pennsylvania State Univ University Park","Standard Grant","Zhilan Feng","07/31/2027","$622,793.00","Hidetoshi Inamine","k-shea@psu.edu","201 OLD MAIN","UNIVERSITY PARK","PA","168021503","8148651372","MPS","112800, 733400","068Z","$0.00","This project will integrate mathematical models and experiments to generate and test key hypotheses on the effects of disturbances on biodiversity. Environmental disturbances that cause mortality, such as fire, drought, and flood, are an important feature of any biological community. Through these changes, disturbances can alter the composition of a community and change how the community functions. Biological communities are increasingly facing novel disturbances, and humans routinely employ disturbances, such as pesticides and logging, to manage and harvest ecosystems. Uncovering the myriad effects of disturbances on communities is therefore important for our understanding and management of any ecosystem. However, a systematic understanding of disturbances has been challenging because they come in many forms and affect every type of community. Our project will employ two novel approaches to overcome this challenge. First, it will directly compare the effects of two broad types of disturbances: pulses, which are short and discrete events, and presses, which are long and sustained events. Second, the project will uncover the effects of disturbances on communities where organisms compete over limited resources as well as in communities where one organism consumes another. The project will use a community of bacteria and their predators which allows for highly controlled experiments, which will then inform field systems. It will also recruit a new generation of scientists into disturbance ecology through a course on student-led research projects, which has been shown to increase STEM retention rates in students across diverse backgrounds.

A critical difference between pulse and press disturbances lies in how communities respond to them over time. To precisely compare the effects of pulse vs. press disturbances, one major challenge is to analyze how variations in dynamics arising from different frequencies and intensities of pulses result in different community outcomes, while controlling for the overall mortality rate over the duration of the disturbance. Consequently, ecologists have historically studied press and pulse disturbances separately. Our recent work, however, has developed novel methods to overcome this challenge. We further hypothesize that pulse and press disturbances can have qualitatively different effects on community dynamics. The project will test these methods and hypotheses by integrating mathematical models of disturbances with microcosm experiments. Using microbial systems, we will: (1) Determine the differential effects of pulse and press disturbances on competitive community dynamics in a single trophic layer using an experimental community of Pseudomonas fluorescens strains; (2) Develop mathematical models to elucidate the effects of pulse and press disturbances on communities with predator-prey interactions; (3) Experimentally analyze the differential effects of pulse and press disturbances on predator-prey dynamics using a protist predator Tetrahymena thermophila of P. fluorescens. Our work generalizes disturbance theory to consumer-resource interactions (e.g., predator-prey, host-pathogen, plant-herbivore), which are ubiquitous and fundamental processes across ecological systems yet often overlooked in the disturbance literature.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2424302","eMB: Collaborative Research: Integrated Hybrid Mathematical Modeling for Schistosomiasis Elimination","DMS","MATHEMATICAL BIOLOGY","09/01/2024","08/13/2024","Yang Yang","GA","University of Georgia","Standard Grant","Amina Eladdadi","08/31/2027","$133,203.00","","yang.yang4@uga.edu","623 BOYD GRADUATE RESEARCH CTR","ATHENS","GA","306020001","7065425939","MPS","733400","8038, 8083","$0.00","This project is a collaboration amongst the University of Florida (Gainesville), the University of Georgia (Athens), and the University of Massachusetts (Amherst).

Schistosomiasis, a disease caused by parasitic worms and transmitted through contact with contaminated freshwater, poses a significant public health threat in many developing regions. Hence, designing effective intervention strategies to mitigate the disease?s impact is timely and critical. This project aims to advance our understanding of schistosomiasis transmission dynamics and control. Specifically focusing on schistosomiasis in Zanzibar and Ethiopia, this research will create and use innovative mathematical modeling tools to understand how various factors like human movement and environmental changes influence disease transmission. This will help to identify the best strategies to control and eventually eliminate schistosomiasis as a public health problem. The project is not only scientifically important but also has significant public health, educational, and societal implications. The educational and societal impacts include training a diverse group of students (including students from underrepresented groups) and fostering interdisciplinary and collaborative research skills. The project will provide novel analytic tools for efficient resource management and inform evidence-based policies for sustainable elimination of schistosomiasis, thereby significantly impacting global health. A workshop in Zanzibar will further help building workforce in quantitative public health and disseminating scientific knowledge.

The proposed project seeks to develop advanced mathematical models to improve our understanding and management of schistosomiasis transmission dynamics, especially during the transition from high to low transmission phases towards elimination. Current models often fail to adequately capture low transmission environments, where random events, spatial and temporal heterogeneities, as well as environmental factors significantly impact transmission persistence. The project aims to develop a novel and robust hybrid deterministic-agent-based modeling framework integrating snail population dynamics (an aspect hither to overlooked in many schistosomiases transmission models) and environmental factors, using data for Schistosoma haematobium from Zanzibar and Schistosoma mansoni from Ethiopia. This innovative dual-phase framework will capture complexities in both high and low transmission settings, incorporating human movement, hydrological networks, and parasite gene flow. The project will assess persistence drivers under low-level transmission, identify transmission breakpoints, and optimize intervention strategies, offering new insights into transmission dynamics and control strategies that lead to impactful public health policies.?

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2424301","eMB: Collaborative Research: Integrated Hybrid Mathematical Modeling for Schistosomiasis Elimination","DMS","MATHEMATICAL BIOLOGY","09/01/2024","08/13/2024","Calistus Ngonghala","FL","University of Florida","Standard Grant","Amina Eladdadi","08/31/2027","$196,163.00","","calistusnn@ufl.edu","1523 UNION RD RM 207","GAINESVILLE","FL","326111941","3523923516","MPS","733400","8038","$0.00","This project is a collaboration amongst the University of Florida (Gainesville), the University of Georgia (Athens), and the University of Massachusetts (Amherst).

Schistosomiasis, a disease caused by parasitic worms and transmitted through contact with contaminated freshwater, poses a significant public health threat in many developing regions. Hence, designing effective intervention strategies to mitigate the disease?s impact is timely and critical. This project aims to advance our understanding of schistosomiasis transmission dynamics and control. Specifically focusing on schistosomiasis in Zanzibar and Ethiopia, this research will create and use innovative mathematical modeling tools to understand how various factors like human movement and environmental changes influence disease transmission. This will help to identify the best strategies to control and eventually eliminate schistosomiasis as a public health problem. The project is not only scientifically important but also has significant public health, educational, and societal implications. The educational and societal impacts include training a diverse group of students (including students from underrepresented groups) and fostering interdisciplinary and collaborative research skills. The project will provide novel analytic tools for efficient resource management and inform evidence-based policies for sustainable elimination of schistosomiasis, thereby significantly impacting global health. A workshop in Zanzibar will further help building workforce in quantitative public health and disseminating scientific knowledge.

The proposed project seeks to develop advanced mathematical models to improve our understanding and management of schistosomiasis transmission dynamics, especially during the transition from high to low transmission phases towards elimination. Current models often fail to adequately capture low transmission environments, where random events, spatial and temporal heterogeneities, as well as environmental factors significantly impact transmission persistence. The project aims to develop a novel and robust hybrid deterministic-agent-based modeling framework integrating snail population dynamics (an aspect hither to overlooked in many schistosomiases transmission models) and environmental factors, using data for Schistosoma haematobium from Zanzibar and Schistosoma mansoni from Ethiopia. This innovative dual-phase framework will capture complexities in both high and low transmission settings, incorporating human movement, hydrological networks, and parasite gene flow. The project will assess persistence drivers under low-level transmission, identify transmission breakpoints, and optimize intervention strategies, offering new insights into transmission dynamics and control strategies that lead to impactful public health policies.?

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2424303","eMB: Collaborative Research: Integrated Hybrid Mathematical Modeling for Schistosomiasis Elimination","DMS","MATHEMATICAL BIOLOGY","09/01/2024","08/13/2024","Song Liang","MA","University of Massachusetts Amherst","Standard Grant","Amina Eladdadi","08/31/2027","$34,536.00","","songliang@umass.edu","101 COMMONWEALTH AVE","AMHERST","MA","010039252","4135450698","MPS","733400","8038","$0.00","This project is a collaboration amongst the University of Florida (Gainesville), the University of Georgia (Athens), and the University of Massachusetts (Amherst).

Schistosomiasis, a disease caused by parasitic worms and transmitted through contact with contaminated freshwater, poses a significant public health threat in many developing regions. Hence, designing effective intervention strategies to mitigate the disease?s impact is timely and critical. This project aims to advance our understanding of schistosomiasis transmission dynamics and control. Specifically focusing on schistosomiasis in Zanzibar and Ethiopia, this research will create and use innovative mathematical modeling tools to understand how various factors like human movement and environmental changes influence disease transmission. This will help to identify the best strategies to control and eventually eliminate schistosomiasis as a public health problem. The project is not only scientifically important but also has significant public health, educational, and societal implications. The educational and societal impacts include training a diverse group of students (including students from underrepresented groups) and fostering interdisciplinary and collaborative research skills. The project will provide novel analytic tools for efficient resource management and inform evidence-based policies for sustainable elimination of schistosomiasis, thereby significantly impacting global health. A workshop in Zanzibar will further help building workforce in quantitative public health and disseminating scientific knowledge.

The proposed project seeks to develop advanced mathematical models to improve our understanding and management of schistosomiasis transmission dynamics, especially during the transition from high to low transmission phases towards elimination. Current models often fail to adequately capture low transmission environments, where random events, spatial and temporal heterogeneities, as well as environmental factors significantly impact transmission persistence. The project aims to develop a novel and robust hybrid deterministic-agent-based modeling framework integrating snail population dynamics (an aspect hither to overlooked in many schistosomiases transmission models) and environmental factors, using data for Schistosoma haematobium from Zanzibar and Schistosoma mansoni from Ethiopia. This innovative dual-phase framework will capture complexities in both high and low transmission settings, incorporating human movement, hydrological networks, and parasite gene flow. The project will assess persistence drivers under low-level transmission, identify transmission breakpoints, and optimize intervention strategies, offering new insights into transmission dynamics and control strategies that lead to impactful public health policies.?

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2424855","eMB: Collaborative Research: Using mathematics to bridge between evolutionary dynamics in the hematopoietic systems of mice and humans: from in vivo to epidemiological scales","DMS","MATHEMATICAL BIOLOGY","10/01/2024","08/08/2024","Angela Fleischman","CA","University of California-Irvine","Standard Grant","Amina Eladdadi","09/30/2027","$116,105.00","","agf@uci.edu","160 ALDRICH HALL","IRVINE","CA","926970001","9498247295","MPS","733400","8038","$0.00","This project is a collaboration between three institutions: University of California-San Diego, Xavier University of Louisiana, and University of California-Irvine. The human blood contains different cell types that are continuously produced, while older cells die. As this process continues while the organism ages, mistakes are made during cell production, generating mutant cells. These mutants can linger in the blood and become more abundant over time. They can contribute to chronic health conditions and there is a chance that they initiate cancer. It is not well understood why these mutant cells persist and expand. One problem that has held back progress is that for obvious reasons it is impossible to perform experiments with human subjects to investigate this. Mathematics combined with epidemiological data, however, offers a way around this limitation. This project develops mathematical models describing the evolution of mutant cells in the blood over time, using experimental mouse data to define the model structure. New mathematical approaches are then used to adapt this model to the human blood system, by bridging between mathematical models of mutant evolution in the blood, and the epidemiological age-incidence of mutants in the human population. There is broad public health impact, since this work can suggest ways to reduce the mutant cells in patients, which can alleviate chronic health conditions and reduce cancer risk. From the educational perspective, the PIs collaborate with Xavier University of Louisiana, an undergraduate historically black university, to foster enthusiasm in continued education and careers in STEM, and equip students with knowledge and skills to potentially continue in graduate programs at top universities, thus promoting social mobility.

As higher organisms age, tissue cells acquire mutations that can rise in frequency over time. Such clonal evolutionary processes have been documented in many human tissues and have become a major focus for understanding the biology of aging. Gaining more insights into mechanisms that drive mutant emergence in non-malignant human tissues is an important biological / public health question that needs to be addressed to define correlates of tissue aging. While experiments in mice have suggested possible drivers of mutant evolution in tissues, a central unresolved question is whether (and how) knowledge from murine models can be applied to humans. Mathematics provides a new approach to address this challenge: We propose a multiscale approach that uses mathematics to bridge between cellular dynamics of mice and humans, by utilizing epidemiological data of mutant incidence in human populations. We use ?clonal hematopoiesis of indeterminate potential? (CHIP) as a study system, where TET2 and DNMT3A mutant clones emerge in the histologically normal hematopoietic system. Based on stem cell transplantation experiments in mice, we seek to construct a predictive mathematical model of mutant evolution in mice. Using the hazard function, this in vivo model can predict the epidemiological incidence of mutants. Fitting predicted to observed mutant age-incidence data for humans will yield a parameterized and predictive model of human TET2 and DNMT3A mutant evolution. Public health impacts include a better understanding of mutant evolution in the human hematopoietic system, which may lead to evolution-based intervention strategies to reduce CHIP mutant burden.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2424684","eMB: Multi-state bootstrap percolation on digraphs as a framework for neuronal network analysis","DMS","IIBR: Infrastructure Innovatio, MATHEMATICAL BIOLOGY","09/01/2024","08/07/2024","Jonathan Rubin","PA","University of Pittsburgh","Standard Grant","Zhilan Feng","08/31/2027","$384,792.00","Gregory Constantine, Mohammad Amin Rahimian, Sabrina Streipert","jonrubin@pitt.edu","4200 FIFTH AVENUE","PITTSBURGH","PA","152600001","4126247400","MPS","084Y00, 733400","068Z, 8038, 8091","$0.00","To study the spread of disease or opinions, it has proven useful to consider a collection of interacting individuals as a mathematical structure called a graph. A graph consists of a set of nodes and a set of edges, each of which links a pair of nodes. PI will extend this framework to the study of neuronal activity. In the neuronal case, each node is a neuron, and edges between them represent the one-way or directed synaptic connections through which neurons interact. Moreover, to capture the different levels of activity that neurons exhibit, each node will be in one of three states, with state changes determined by interactions along edges. PI will develop novel mathematical methods to analyze the patterns of activity that emerge in such multi-state, directed graphs. These methods will allow the project team to study how activity spreads in networks of neurons, how this spread depends on the connection patterns in the network, and what properties characterize sets of nodes that are especially effective at spreading activity. The research results will generate novel predictions about the properties and function of networks of neurons in the brain, with a focus on the key networks that drive breathing and other essential, rhythmic behaviors. The project will train students, will generate openly available computer code, and will include public outreach through online videos and a summer math program for girls.

Functional outputs from brain circuits driving certain critical, rhythmic behaviors require the widespread emergence of an elevated, bursting state of neuronal activity. The main goal of this project is to advance knowledge about how the localized initiation of activity can rapidly evolve into widespread bursting in synaptically coupled neuronal networks, exemplified by the respiratory brainstem circuit. The project team will achieve this goal by representing such networks as digraphs in which each node can assume one of three possible activity states ? inactive, weakly active, and fully active or bursting -- with updates based on in-neighbors? states. Little theory exists to characterize this multi-state bootstrap percolation framework, and we will develop new analytical approaches involving mean field and master equations, asymptotic and probabilistic estimates, and graph design based on combinatorial principles. The analysis will address differences between dynamics in this framework and that in bootstrap percolation with only two possible states per node, the impact of global graph properties on activity spread, and the characteristics of local initiation sites that result in especially effective activity propagation. Overall, the project will support a new interdisciplinary collaboration and the completed work, involving trainee mentorship and open sharing of code, will provide important insights and predictions about neuronal dynamics and interactions as well as a range of mathematical advances.

This project is jointly funded by the Mathematical Biology Program in the Division of Mathematical Sciences and the Research Resources Cluster in the Division of Biological Infrastructure in the Directorate for Biological Sciences.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2424605","eMB: Collaborative Research: Transmission, Control and Risk Assessment of Chikungunya: Combining Machine Learning with Deterministic Models","DMS","MATHEMATICAL BIOLOGY","09/01/2024","08/09/2024","Shigui Ruan","FL","University of Miami","Standard Grant","Lisa Gayle Davis","08/31/2027","$323,038.00","Xi Huo, Han Li","ruan@math.miami.edu","1320 SOUTH DIXIE HIGHWAY STE 650","CORAL GABLES","FL","331462919","3052843924","MPS","733400","079Z, 8038","$0.00","This is a collaborative project among the University of Miami, Indiana University and Nova Southeastern University. Chikungunya (CHIK) is a viral disease transmitted to humans through the bites of mosquitoes infected with the chikungunya virus (CHIKV). CHIKV is endemic in Central and South American countries, posing significant public health burdens. As the ?gateway to Latin America?, Miami-Dade County, Florida, has seen annual importations of CHIKV cases over the last decade. Miami-Dade County has an abundant population of Aedes mosquitoes, a suitable climate that promotes the growth of these mosquito vector species, and the potential for local CHIKV circulation. Integrating Aedes mosquito data collected in Miami-Dade County and local CHIK outbreak data from Brazil into a hybrid machine learning and mathematical modeling framework, the investigative team will reconstruct CHIKV dynamics in Brazil and evaluate control efforts in Florida. The project will further assess the risk for importation and local transmission of CHIKV in Florida considering global environmental changes. This study will provide valuable insights into the transmission dynamics of CHIKV and assist in developing more effective preventive and control measures. Findings can increase preparedness to anticipate and respond to other reemerging arboviruses such as dengue virus and yellow fever virus, as well as similar arboviruses yet to emerge. The project includes various activities for interdisciplinary training of undergraduate students, graduate students, and postdoctoral fellows. Networking activities are planned to encourage collaboration between researchers, especially young researchers from historically underrepresented groups in mathematics.

The project aims to develop a novel method that integrates differential equations and machine learning techniques to incorporate complex features into traditional ecological and epidemic models. This method aims to: (i) identify climate and environmental factors affecting Aedes mosquito population growth; (ii) provide accurate projections on vector abundance to design mosquito control measures; (iii) reconstruct local transmission of CHIKV during recent outbreaks in Brazil; (iv) model the importation of CHIKV into Florida and the transmission of CHIKV from imported cases to local mosquitoes; (v) investigate how global environmental change may affect the population dynamics of Aedes mosquitoes and the local spread of CHIKV in South Florida. The obtained results will improve preparedness and response also for other emerging and reemerging arboviruses, such as the dengue virus, Zika virus, and yellow fever virus.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2424854","eMB: Collaborative Research: Using mathematics to bridge between evolutionary dynamics in the hematopoietic systems of mice and humans: from in vivo to epidemiological scales","DMS","MATHEMATICAL BIOLOGY","10/01/2024","08/08/2024","Timmy Ma","LA","Xavier University of Louisiana","Standard Grant","Amina Eladdadi","09/30/2027","$36,644.00","","tma@xula.edu","1 DREXEL DR","NEW ORLEANS","LA","701251056","5045205440","MPS","733400","8038, 9150","$0.00","This project is a collaboration between three institutions: University of California-San Diego, Xavier University of Louisiana, and University of California-Irvine. The human blood contains different cell types that are continuously produced, while older cells die. As this process continues while the organism ages, mistakes are made during cell production, generating mutant cells. These mutants can linger in the blood and become more abundant over time. They can contribute to chronic health conditions and there is a chance that they initiate cancer. It is not well understood why these mutant cells persist and expand. One problem that has held back progress is that for obvious reasons it is impossible to perform experiments with human subjects to investigate this. Mathematics combined with epidemiological data, however, offers a way around this limitation. This project develops mathematical models describing the evolution of mutant cells in the blood over time, using experimental mouse data to define the model structure. New mathematical approaches are then used to adapt this model to the human blood system, by bridging between mathematical models of mutant evolution in the blood, and the epidemiological age-incidence of mutants in the human population. There is broad public health impact, since this work can suggest ways to reduce the mutant cells in patients, which can alleviate chronic health conditions and reduce cancer risk. From the educational perspective, the PIs collaborate with Xavier University of Louisiana, an undergraduate historically black university, to foster enthusiasm in continued education and careers in STEM, and equip students with knowledge and skills to potentially continue in graduate programs at top universities, thus promoting social mobility.

As higher organisms age, tissue cells acquire mutations that can rise in frequency over time. Such clonal evolutionary processes have been documented in many human tissues and have become a major focus for understanding the biology of aging. Gaining more insights into mechanisms that drive mutant emergence in non-malignant human tissues is an important biological / public health question that needs to be addressed to define correlates of tissue aging. While experiments in mice have suggested possible drivers of mutant evolution in tissues, a central unresolved question is whether (and how) knowledge from murine models can be applied to humans. Mathematics provides a new approach to address this challenge: We propose a multiscale approach that uses mathematics to bridge between cellular dynamics of mice and humans, by utilizing epidemiological data of mutant incidence in human populations. We use ?clonal hematopoiesis of indeterminate potential? (CHIP) as a study system, where TET2 and DNMT3A mutant clones emerge in the histologically normal hematopoietic system. Based on stem cell transplantation experiments in mice, we seek to construct a predictive mathematical model of mutant evolution in mice. Using the hazard function, this in vivo model can predict the epidemiological incidence of mutants. Fitting predicted to observed mutant age-incidence data for humans will yield a parameterized and predictive model of human TET2 and DNMT3A mutant evolution. Public health impacts include a better understanding of mutant evolution in the human hematopoietic system, which may lead to evolution-based intervention strategies to reduce CHIP mutant burden.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2424607","eMB: Collaborative Research: Transmission, Control and Risk Assessment of Chikungunya: Combining Machine Learning with Deterministic Models","DMS","MATHEMATICAL BIOLOGY","09/01/2024","08/09/2024","Jing Chen","FL","Nova Southeastern University","Standard Grant","Lisa Gayle Davis","08/31/2027","$57,287.00","","jchen1@nova.edu","3300 S UNIVERSITY DR","FT LAUDERDALE","FL","333282004","9542625366","MPS","733400","079Z, 8038","$0.00","This is a collaborative project among the University of Miami, Indiana University and Nova Southeastern University. Chikungunya (CHIK) is a viral disease transmitted to humans through the bites of mosquitoes infected with the chikungunya virus (CHIKV). CHIKV is endemic in Central and South American countries, posing significant public health burdens. As the ?gateway to Latin America?, Miami-Dade County, Florida, has seen annual importations of CHIKV cases over the last decade. Miami-Dade County has an abundant population of Aedes mosquitoes, a suitable climate that promotes the growth of these mosquito vector species, and the potential for local CHIKV circulation. Integrating Aedes mosquito data collected in Miami-Dade County and local CHIK outbreak data from Brazil into a hybrid machine learning and mathematical modeling framework, the investigative team will reconstruct CHIKV dynamics in Brazil and evaluate control efforts in Florida. The project will further assess the risk for importation and local transmission of CHIKV in Florida considering global environmental changes. This study will provide valuable insights into the transmission dynamics of CHIKV and assist in developing more effective preventive and control measures. Findings can increase preparedness to anticipate and respond to other reemerging arboviruses such as dengue virus and yellow fever virus, as well as similar arboviruses yet to emerge. The project includes various activities for interdisciplinary training of undergraduate students, graduate students, and postdoctoral fellows. Networking activities are planned to encourage collaboration between researchers, especially young researchers from historically underrepresented groups in mathematics.

The project aims to develop a novel method that integrates differential equations and machine learning techniques to incorporate complex features into traditional ecological and epidemic models. This method aims to: (i) identify climate and environmental factors affecting Aedes mosquito population growth; (ii) provide accurate projections on vector abundance to design mosquito control measures; (iii) reconstruct local transmission of CHIKV during recent outbreaks in Brazil; (iv) model the importation of CHIKV into Florida and the transmission of CHIKV from imported cases to local mosquitoes; (v) investigate how global environmental change may affect the population dynamics of Aedes mosquitoes and the local spread of CHIKV in South Florida. The obtained results will improve preparedness and response also for other emerging and reemerging arboviruses, such as the dengue virus, Zika virus, and yellow fever virus.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2424004","eMB: Explainable and Physics-Informed Machine Learning for Cell Typing via a Modern Optimization Lens","DMS","OFFICE OF MULTIDISCIPLINARY AC, Innovation: Bioinformatics, MATHEMATICAL BIOLOGY","09/01/2024","08/05/2024","Can Li","IN","Purdue University","Standard Grant","Amina Eladdadi","08/31/2027","$376,162.00","Xiaoping Bao","canli@purdue.edu","2550 NORTHWESTERN AVE # 1100","WEST LAFAYETTE","IN","479061332","7654941055","MPS","125300, 164Y00, 733400","068Z, 075Z, 079Z, 8038","$0.00","Human-induced pluripotent stem cells (hiPSCs) represent a groundbreaking advancement in stem cell research. Derived from skin or blood cells, hiPSCs are reprogrammed to an embryonic-like state, enabling them to differentiate into any cell type, such as blood, immune, heart, and neuron cells. This Nobel Prize-winning technology circumvents the ethical issues associated with human embryonic stem cells and provides valuable models for studying human development, disease, drug testing, and potential cell-based therapies. However, to leverage hiPSCs in clinical settings and large-scale manufacturing, there are significant challenges to overcome. One major challenge is accurately identifying cell types at different stages of differentiation, which is crucial for ensuring the cells perform their intended functions. Traditional experimental methods for cell identification can be costly, time-consuming, and limited in robustness. This research aims to address these challenges by developing explainable and physics-informed machine learning models. These models will enhance the accuracy and reliability of cell type identification, ensuring that hiPSC technology can be widely adopted in clinical and industrial applications, ultimately benefiting society through improved healthcare solutions and advancing our understanding of human biology. The project will involve both graduate and undergraduate students, with graduate students focusing on core theory and method development while undergraduates investigate applications. The PIs will work with Purdue?s Research Experience for Undergraduates (REU), and Summer Vertically Integrated Projects (VIP) program to mentor additional underrepresented minority students each summer to work on interdisciplinary research in stem cell engineering and machine learning. Outreach activities will include developing hands-on K-12 activities, partnering with local organizations, organizing lab tours, and presenting research at the ""Mending Broken Hearts"" gallery exhibit, aiming to increase STEM participation among underrepresented groups.

This research project addresses critical challenges in the adoption and scalability of human-induced pluripotent stem cells (hiPSCs) by developing novel machine learning methodologies. The specific problems targeted include the need for high-accuracy, cost-effective cell type identification during differentiation and the incorporation of prior biological knowledge into explaining machine learning models. The PIs intend to create explainable machine learning algorithms that leverage single-cell RNA sequencing (scRNA-seq) and imaging data to provide counterfactual explanations, highlighting key genes or image features critical for cell typing. These models will utilize mixed-integer programming to solve counterfactual explanations to generate interpretable predictions, addressing the limitations of current black-box approaches. Additionally, the aim is to overcome data scarcity by integrating biological knowledge into the machine learning frameworks, employing novel physics-informed machine learning algorithms. This research will develop and benchmark these innovative methods, applying them to the study of Tumor Associated Neutrophils (TANs) for cancer therapy. By enhancing explainability in cell typing predictions, this work will significantly advance the field of stem cell research and its applications in regenerative medicine and oncology.

This project is jointly funded by the Mathematical Biology Program in the Division of Mathematical Sciences, the Infrastructure Innovation for Biological Research in the Division of Biological Infrastructure (BIO/DBI), and Office of Strategic Initiatives.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2424606","eMB: Collaborative Research: Transmission, Control and Risk Assessment of Chikungunya: Combining Machine Learning with Deterministic Models","DMS","MATHEMATICAL BIOLOGY","09/01/2024","08/09/2024","Marco Ajelli","IN","Indiana University","Standard Grant","Lisa Gayle Davis","08/31/2027","$78,237.00","Andre Wilke","majelli@iu.edu","107 S INDIANA AVE","BLOOMINGTON","IN","474057000","3172783473","MPS","733400","079Z, 8038","$0.00","This is a collaborative project among the University of Miami, Indiana University and Nova Southeastern University. Chikungunya (CHIK) is a viral disease transmitted to humans through the bites of mosquitoes infected with the chikungunya virus (CHIKV). CHIKV is endemic in Central and South American countries, posing significant public health burdens. As the ?gateway to Latin America?, Miami-Dade County, Florida, has seen annual importations of CHIKV cases over the last decade. Miami-Dade County has an abundant population of Aedes mosquitoes, a suitable climate that promotes the growth of these mosquito vector species, and the potential for local CHIKV circulation. Integrating Aedes mosquito data collected in Miami-Dade County and local CHIK outbreak data from Brazil into a hybrid machine learning and mathematical modeling framework, the investigative team will reconstruct CHIKV dynamics in Brazil and evaluate control efforts in Florida. The project will further assess the risk for importation and local transmission of CHIKV in Florida considering global environmental changes. This study will provide valuable insights into the transmission dynamics of CHIKV and assist in developing more effective preventive and control measures. Findings can increase preparedness to anticipate and respond to other reemerging arboviruses such as dengue virus and yellow fever virus, as well as similar arboviruses yet to emerge. The project includes various activities for interdisciplinary training of undergraduate students, graduate students, and postdoctoral fellows. Networking activities are planned to encourage collaboration between researchers, especially young researchers from historically underrepresented groups in mathematics.

The project aims to develop a novel method that integrates differential equations and machine learning techniques to incorporate complex features into traditional ecological and epidemic models. This method aims to: (i) identify climate and environmental factors affecting Aedes mosquito population growth; (ii) provide accurate projections on vector abundance to design mosquito control measures; (iii) reconstruct local transmission of CHIKV during recent outbreaks in Brazil; (iv) model the importation of CHIKV into Florida and the transmission of CHIKV from imported cases to local mosquitoes; (v) investigate how global environmental change may affect the population dynamics of Aedes mosquitoes and the local spread of CHIKV in South Florida. The obtained results will improve preparedness and response also for other emerging and reemerging arboviruses, such as the dengue virus, Zika virus, and yellow fever virus.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2424004","eMB: Explainable and Physics-Informed Machine Learning for Cell Typing via a Modern Optimization Lens","DMS","OFFICE OF MULTIDISCIPLINARY AC, Innovation: Bioinformatics, MATHEMATICAL BIOLOGY","09/01/2024","08/05/2024","Can Li","IN","Purdue University","Standard Grant","Amina Eladdadi","08/31/2027","$376,162.00","Xiaoping Bao","canli@purdue.edu","2550 NORTHWESTERN AVE # 1100","WEST LAFAYETTE","IN","479061332","7654941055","MPS","125300, 164Y00, 733400","068Z, 075Z, 079Z, 8038","$0.00","Human-induced pluripotent stem cells (hiPSCs) represent a groundbreaking advancement in stem cell research. Derived from skin or blood cells, hiPSCs are reprogrammed to an embryonic-like state, enabling them to differentiate into any cell type, such as blood, immune, heart, and neuron cells. This Nobel Prize-winning technology circumvents the ethical issues associated with human embryonic stem cells and provides valuable models for studying human development, disease, drug testing, and potential cell-based therapies. However, to leverage hiPSCs in clinical settings and large-scale manufacturing, there are significant challenges to overcome. One major challenge is accurately identifying cell types at different stages of differentiation, which is crucial for ensuring the cells perform their intended functions. Traditional experimental methods for cell identification can be costly, time-consuming, and limited in robustness. This research aims to address these challenges by developing explainable and physics-informed machine learning models. These models will enhance the accuracy and reliability of cell type identification, ensuring that hiPSC technology can be widely adopted in clinical and industrial applications, ultimately benefiting society through improved healthcare solutions and advancing our understanding of human biology. The project will involve both graduate and undergraduate students, with graduate students focusing on core theory and method development while undergraduates investigate applications. The PIs will work with Purdue?s Research Experience for Undergraduates (REU), and Summer Vertically Integrated Projects (VIP) program to mentor additional underrepresented minority students each summer to work on interdisciplinary research in stem cell engineering and machine learning. Outreach activities will include developing hands-on K-12 activities, partnering with local organizations, organizing lab tours, and presenting research at the ""Mending Broken Hearts"" gallery exhibit, aiming to increase STEM participation among underrepresented groups.

This research project addresses critical challenges in the adoption and scalability of human-induced pluripotent stem cells (hiPSCs) by developing novel machine learning methodologies. The specific problems targeted include the need for high-accuracy, cost-effective cell type identification during differentiation and the incorporation of prior biological knowledge into explaining machine learning models. The PIs intend to create explainable machine learning algorithms that leverage single-cell RNA sequencing (scRNA-seq) and imaging data to provide counterfactual explanations, highlighting key genes or image features critical for cell typing. These models will utilize mixed-integer programming to solve counterfactual explanations to generate interpretable predictions, addressing the limitations of current black-box approaches. Additionally, the aim is to overcome data scarcity by integrating biological knowledge into the machine learning frameworks, employing novel physics-informed machine learning algorithms. This research will develop and benchmark these innovative methods, applying them to the study of Tumor Associated Neutrophils (TANs) for cancer therapy. By enhancing explainability in cell typing predictions, this work will significantly advance the field of stem cell research and its applications in regenerative medicine and oncology.

This project is jointly funded by the Mathematical Biology Program in the Division of Mathematical Sciences, the Infrastructure Innovation for Biological Research in the Division of Biological Infrastructure (BIO/DBI), and Office of Strategic Initiatives.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2424748","eMB: Multi-task biologically informed neural networks for learning dynamical systems from single-cell protein expression data","DMS","MATHEMATICAL BIOLOGY","09/01/2024","08/08/2024","Kevin Flores","NC","North Carolina State University","Standard Grant","Amina Eladdadi","08/31/2027","$317,533.00","Orlando Arguello-Miranda","kbflores@ncsu.edu","2601 WOLF VILLAGE WAY","RALEIGH","NC","276950001","9195152444","MPS","733400","075Z, 079Z, 8038","$0.00","A fundamental unanswered biological question with biomedical and industrial relevance is how cells integrate external information from multiple biochemical pathways to enter and exit quiescence in response to stress. Non-destructive measurements of single-cell protein expression in yeast cells have revealed that signaling in quiescence-related biochemical pathways can be highly heterogeneous across genetically identical cell populations as they transition into dormancy, even though they are treated with the exact same stress type and timing. Mathematical modeling has produced remarkable insights into the protein interaction networks that govern the yeast cell cycle and quiescence, however, predicting the transition from proliferation into quiescence at the single-cell level remains unclear under most physiological scenarios. The goal of this project is to develop a mathematical model that recapitulates the heterogeneity in proliferation/quiescence transitions of yeast cells in response to multiple quiescence-promoting stimuli. To accomplish this goal, this project will couple the development of novel scientific machine learning methods, chemical and environmental perturbation experiments, and single-cell protein expression measurements in live yeast cells. This research will address the mathematical challenges of learning and validating mathematical models from heterogeneous high-dimensional time series data to answer significant questions about how signaling pathways govern cell fate and differentiation. The project?s findings will be applicable to quiescence-related phenomena such as chemotherapy-resistant quiescent cancer cells, stem cells that exit quiescence for wound healing, and developmental processes that rely on the ubiquitous stress signaling pathways that will be studied. Research findings will be communicated to the scientific community through conference workshops and minisymposia, and to the general public through the creation of new K-12 outreach exhibits.

The proposed work will develop a data-driven mathematical framework to mechanistically explain inter-cellular variability during proliferation-quiescence transitions. Specifically, new deep learning tools will be developed to directly learn differential equation models from multivariate protein expression data collected from individual yeast cells undergoing quiescence in response to a diverse range of biologically relevant stressors. These research efforts will involve the integration of recurrent neural networks, multi-task learning, and novel regularization methods that enable deep learning models to simultaneously learn differential equations from thousands of single-cell replicates of protein expression time series data. Sensitivity analysis methods will be developed in conjunction with these new deep learning tools to enable optimization within a vast space of stress combinations and timing, thereby generating quantitative predictions about which experimental perturbations have the greatest effect on inter-cellular phenotype variability. The application of the new framework to non-destructive single-cell data arising from state-of-the-art experimental setups will shed new light on how coordinated cell division, stress, and metabolic signaling pathways produce intercellular variability in protein expression and quiescence phenotypes observed across species. In addition, this project will provide interdisciplinary training to graduate and undergraduate students, and develop open-source code for application to biological data sets involving perturbation experiments with multivariate time series data.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2436120","MPOPHC: Integrating human risk perception and social processes into policy responses in an epidemiological model","DMS","OFFICE OF MULTIDISCIPLINARY AC, MATHEMATICAL BIOLOGY, ","10/01/2024","08/07/2024","Brian Beckage","VT","University of Vermont & State Agricultural College","Standard Grant","Zhilan Feng","09/30/2027","$1,344,200.00","Suzanne Lenhart, Charles Sims, Katherine Lacasse","Brian.Beckage@uvm.edu","85 S PROSPECT STREET","BURLINGTON","VT","054051704","8026563660","MPS","125300, 733400, Y20600","008Z, 9150, 9178, 9179","$0.00","Epidemics arise from interactions between pathogens and human hosts, where the pathogen influences human behavior and human behavior influences the spread of the pathogen. The models used to predict pathogen spread do not include the complexity of interactions between disease and human behavior but instead focus on biological processes and policy interventions. However, disease transmission depends on people?s behaviors, which are shaped by their perceptions of risk from the disease and from health interventions, as well as by the opinions and behaviors of the other people around them. This project will contribute to the development of mathematical epidemiological models that better represent the complexities of the human response to disease and that can be used to evaluate the relative impacts of public health policies on disease dynamics. The project will be focused on understanding respiratory diseases such as COVID-19, seasonal flu, and bird flu, but can be readily modified to be broadly applicable to other infectious diseases such as HIV or Ebola. The project will contribute to existing national COVID-19 and Flu Scenario Modeling Hubs that are working to better predict and understand the dynamics of infectious disease and to contribute to policy interventions. The Investigators will disseminate the results and foster connections with the disease modeling community through a workshop for public health professionals and will engage the public through production of educational music videos targeted at the broader community

The complexity of human behavior is not well represented in epidemiological models, contributing to reduced skill and utility of model forecasts. While some epidemiological models represent human behavioral responses using a few static parameters, the Investigators will construct models of human behavior and policy processes that update dynamically to represent the dependence of human responses to the evolving state of the epidemic. Human cognition, social and policy responses will be represented using a system of differential equations linked with a traditional Susceptible-Exposed-Infected-Recovered epidemiological model using infectious respiratory diseases such as SARS-CoV-2 and H5N1 as model systems. Adoption of protective behaviors (vaccination, physical distancing) will be a function of risk perceptions (from disease and health interventions), health policies (lockdowns, vaccine mandates), and the behavior of other people (social norms). Policy interventions and adoption of protective behaviors mediate disease spread and impacts (infections and deaths) that influence human behavioral and policy responses. Mathematical novelty arises because cognition depends upon the history of infection, so the differential equations have past-dependence, generating differential integral equations. Model outputs will be used to analyze the sensitivity of and uncertainty in epidemic forecasts that arise from human risk perceptions, social influence, protective behaviors, and policy interventions. This project will advance the disease modeling community?s capability to analyze the interlinked dynamics of human social systems and infectious disease, increase the impact of social science on the disease modeling community, and will develop analysis methods for the complex and time-dependent interactions that arise from linkages of disease dynamics with social systems.

This award is co-funded by the NSF Division of Mathematical Sciences (DMS) and the CDC Coronavirus and Other Respiratory Viruses Division (CORVD).

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2432168","Conference: Interagency Analysis and Modeling Group/Multiscale Modeling Consortium (IMAG/MSM) Meeting on Operationalizing the NASEM Report on Digital Twins","DMS","STATISTICS, COMPUTATIONAL MATHEMATICS, MATHEMATICAL BIOLOGY","08/15/2024","08/02/2024","Gary An","VT","University of Vermont & State Agricultural College","Standard Grant","Troy D. Butler","07/31/2025","$30,000.00","","gan@med.med.edu","85 S PROSPECT STREET","BURLINGTON","VT","054051704","8026563660","MPS","126900, 127100, 733400","075Z, 079Z, 7556, 9150","$0.00","On December 15, 2023, The National Academies of Sciences, Engineering and Medicine (NASEM) released a report entitled: ?Foundational Research Gaps and Future Directions for Digital Twins? (?NASEM DT REPORT?). The purpose of this report was to bring structure to the burgeoning field of digital twins by providing a working definition and a series of research challenges that need to be addressed to allow this technology to fulfill its full potential. The concept of digital twins is compelling and has the potential to impact a broad range of domains. For instance, digital twins have either been proposed or are currently being developed for manufactured devices, buildings, cities, ecologies and the Earth as a whole. It is natural that the concept be applied to biology and medicine, as the most recognizable concept of a ?twin? is that of identical human twins. The application of digital twins to biomedicine also follows existing trends of Personalized and Precision medicine, in short: ?the right treatment for the right person at the right time.? Fulfilling the promise of biomedical digital twins will require multidisciplinary Team Science that brings together various experts from fields as diverse as medicine, computer science, engineering, biological research, advanced mathematics and ethics. The purpose of this conference, the ?2024 Interagency Modeling and Analysis Group (IMAG)/Multiscale Modeling (MSM) Consortium Meeting: Setting up Teams for Biomedical Digital Twins,? is to do exactly this: bringing together such needed expertise in a series of teaming exercises to operationalize the findings of the NASEM DT REPORT in the context of biomedical digital twins. As part of outreach and training efforts to broaden the participation within this growing field, this workshop will provide support for both traditionally under-represented categories of senior researchers as well as junior researchers such as graduate students and postdoctoral researchers.

Facilitating the development and deployment of biomedical digital twins requires operationalizing the findings and recommendations of the NASEM DT REPORT, which raises a series of specific and unique challenges in the biomedical domain. More specifically, there are numerous steps that need to be taken to convert the highly complex simulation models of biological processes developed by members of the MSM Consortium into biomedical digital twins that are compliant with the definition of digital twins presented in the NASEM DT REPORT. There are also identified challenges associated with these various steps. Some of these challenges can benefit from lessons learned in other domains that have developed digital twins while others will require the development of new techniques in the fields of statistics, computational mathematics and mathematical biology. This task will require multidisciplinary collaborations between mathematicians, computational researchers, experimental biologists and clinicians. This IMAG/MSM meeting will promote the concepts of Team Science to bring together experienced multiscale modeling researchers and experts from the mathematical, statistical, computational, experimental and clinical communities to form the multidisciplinary teams needed to operationalize the findings of the NASEM DT REPORT. The website for this meeting is at https://www.imagwiki.nibib.nih.gov/news-events/announcements/2024-imagmsm-meeting-september-30-october-2-2024, with the landing page for the Interagency Modeling and Analysis Group at https://www.imagwiki.nibib.nih.gov/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2419308","Conference: Ninth International Conference on Mathematical Modeling and Analysis of Populations in Biological Systems","DMS","MATHEMATICAL BIOLOGY","08/01/2024","07/31/2024","Peter Hinow","WI","University of Wisconsin-Milwaukee","Standard Grant","Amina Eladdadi","07/31/2025","$20,000.00","Gabriella Pinter, Istvan Lauko","hinow@uwm.edu","3203 N DOWNER AVE # 273","MILWAUKEE","WI","532113188","4142294853","MPS","733400","7556","$0.00","The Ninth International Conference on Mathematical Modeling and Analysis of Populations in Biological Systems (ICMA-IX) will be held at the University of Wisconsin - Milwaukee, on October 18 - 19, 2024. ICMA-IX builds upon the success of eight previous conferences, each of which had over 100 participants. The aim of this conference is to have participants from a wide variety of backgrounds, various career levels, and from underrepresented groups. The conference will highlight significant recent developments in mathematical biology and provide a forum for the participants to meet, to communicate their scientific discoveries, and to initiate new collaborations. By bringing together a new generation of researchers along with the established experts, the aim is to cultivate new collaborations and networks that can help junior researchers as they advance their careers.

Mathematical modeling in biology and medicine is becoming ever more important and impactful. This became more visible than ever to the general public during the years of the recent Covid-19 pandemic when crucial policy recommendations were made by epidemiologists and modelers based on mathematical models of the dynamics of the disease. Further applications include a better understanding of cancer spread and its treatment, the working of the nervous system and interactions of species in ecosystems at various scales. ICMA-IX will continue the tradition of including a plenary talk based on the paper that won the Lord May Prize awarded by the Journal of Biological Dynamics. The conference will feature mathematical modeling in biology diverse in both its applications and its techniques. By its very nature, this research is interdisciplinary and collaborative. Thus, conferences are crucial events to bring together researchers and students from different areas.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2425995","Conference: The SIAM Quantum Intersections Convening","DMS","FET-Fndtns of Emerging Tech, OFFICE OF MULTIDISCIPLINARY AC, INFRASTRUCTURE PROGRAM, APPLIED MATHEMATICS, TOPOLOGY, FOUNDATIONS, STATISTICS, QIS - Quantum Information Scie, MATHEMATICAL BIOLOGY","08/01/2024","07/31/2024","Suzanne Weekes","PA","Society For Industrial and Applied Math (SIAM)","Standard Grant","Tomek Bartoszynski","07/31/2025","$349,996.00","","weekes@siam.org","3600 MARKET ST FL 6","PHILADELPHIA","PA","191042669","2153829800","MPS","089Y00, 125300, 126000, 126600, 126700, 126800, 126900, 728100, 733400","7203, 7556","$0.00","Society for Industrial and Applied Mathematics (SIAM) will host the SIAM Quantum Intersections Convening - Integrating Mathematical Scientists into Quantum Research to bring quantum-curious mathematical scientists together with leading experts in quantum science for a three-day interactive workshop. Recognizing the critical role of mathematical scientists, this convening aims to promote multidisciplinary collaborations that bridge the gap between mathematics and quantum sciences and aims to foster and increase the involvement and visibility of mathematicians and statisticians in quantum science research and education. The convening will be organized by a steering committee and will be supported by professional facilitators. Participants will learn from and connect with physicists, computer scientists, engineers and mathematical scientists who are experts in quantum science. This in-person gathering will be held in fall 2024 in the Washington DC area. A primary deliverable from the convening will be a report summarizing the activities and recommendations generated during the event. Key presentations will be recorded and will be available on a SIAM webpage.

Society for Industrial and Applied Mathematics (SIAM) will host this convening with the goals of (i) making more mathematical scientists aware of the demand for their expertise in quantum research and articulating areas and problems where they can contribute, (ii) increasing the participation of researchers in mathematical sciences in the quantum information science revolution to accelerate its research and development, (iii) providing a seeding ground for partnerships and collaborations of mathematical scientists with physicists, computer scientists, and engineers from industry and academia, and (iv) recommending activities to develop a quantum science and technology workforce pipeline in the mathematical and computational sciences. A few topics in quantum science where mathematics can help research and discovery include quantum computing, quantum algorithms, quantum optimization, quantum error corrections, quantum information theory, quantum cryptography, quantum sensing and metrology, and quantum networks.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2419308","Conference: Ninth International Conference on Mathematical Modeling and Analysis of Populations in Biological Systems","DMS","MATHEMATICAL BIOLOGY","08/01/2024","07/31/2024","Peter Hinow","WI","University of Wisconsin-Milwaukee","Standard Grant","Amina Eladdadi","07/31/2025","$20,000.00","Gabriella Pinter, Istvan Lauko","hinow@uwm.edu","3203 N DOWNER AVE # 273","MILWAUKEE","WI","532113188","4142294853","MPS","733400","7556","$0.00","The Ninth International Conference on Mathematical Modeling and Analysis of Populations in Biological Systems (ICMA-IX) will be held at the University of Wisconsin - Milwaukee, on October 18 - 19, 2024. ICMA-IX builds upon the success of eight previous conferences, each of which had over 100 participants. The aim of this conference is to have participants from a wide variety of backgrounds, various career levels, and from underrepresented groups. The conference will highlight significant recent developments in mathematical biology and provide a forum for the participants to meet, to communicate their scientific discoveries, and to initiate new collaborations. By bringing together a new generation of researchers along with the established experts, the aim is to cultivate new collaborations and networks that can help junior researchers as they advance their careers.

Mathematical modeling in biology and medicine is becoming ever more important and impactful. This became more visible than ever to the general public during the years of the recent Covid-19 pandemic when crucial policy recommendations were made by epidemiologists and modelers based on mathematical models of the dynamics of the disease. Further applications include a better understanding of cancer spread and its treatment, the working of the nervous system and interactions of species in ecosystems at various scales. ICMA-IX will continue the tradition of including a plenary talk based on the paper that won the Lord May Prize awarded by the Journal of Biological Dynamics. The conference will feature mathematical modeling in biology diverse in both its applications and its techniques. By its very nature, this research is interdisciplinary and collaborative. Thus, conferences are crucial events to bring together researchers and students from different areas.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350184","Dynamical Systems with a View towards Applications","DMS","ANALYSIS PROGRAM, MATHEMATICAL BIOLOGY","07/01/2024","04/10/2024","Lai-Sang Young","NY","New York University","Continuing Grant","Marian Bocea","06/30/2029","$375,506.00","","lsy@cims.nyu.edu","70 WASHINGTON SQ S","NEW YORK","NY","100121019","2129982121","MPS","128100, 733400","5916, 5918, 5936, 5946, 7406","$0.00","The project will broaden the reach of the existing mathematical theory of dynamical systems, and will contribute to bridging the gap between theory and application. The theory of dynamical systems lies at the crossroads of several areas of mathematics, and has natural applications to engineering and to other scientific disciplines. In this project, the principal investigator will extend relevant dynamical results from the finite dimensional case to the infinite dimensional case. These include results about dynamical semi-flows generated by evolutionary partial differential equations. Such equations model a variety of physical phenomena. A second component of the project consists in leveraging the principal investigator?s expertise in interdisciplinary research to identify recurrent themes and emergent phenomena arising naturally in the biological sciences, thereby incorporating new phenomenology into a modern theory of dynamical systems. In addition to these scientific advances, the proposed projects offer ample training opportunities for students and postdocs.

The project centers on four lines of research. The first two lines seek to extend finite-dimensional phenomena to infinite dimensions. In the first project, the principal investigator aims to show that in the presence of random forces, a unifying description of large-time orbit distribution holds much more generally than is currently known. The second project seeks to extract low dimensional structures and dynamical phenomena embedded in high dimensions. Specifically, the PI will aim to show that shear-induced chaos is a source of instability in physical models including the Navier-Stokes system. The remaining two projects investigate a class of reaction networks of relevance to biology. Mean-field approaches to the large-time behavior of scalable networks will be investigated. The project also aims to study the novel concept of `depletion?, a bifurcation phenomenon amenable to mathematical analysis. From the viewpoint of applications, depletion occurs naturally in several contexts and potentially has dire biological consequences. The final project seeks to use scalable reaction networks as a model to answer a question of fundamental importance for dissipative dynamical systems, namely, which invariant measures are visible from an observational viewpoint?

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413769","Connecting ecosystem models with evolutionary genetics: Fitness landscapes, persistent networks, and phylodynamic simulation","DMS","MATHEMATICAL BIOLOGY","08/01/2024","07/31/2024","Cameron Browne","LA","University of Louisiana at Lafayette","Standard Grant","Zhilan Feng","07/31/2027","$261,226.00","","cxb0559@louisiana.edu","104 E UNIVERSITY AVE","LAFAYETTE","LA","705032014","3374825811","MPS","733400","9150","$0.00","The evolution of ecological networks depends on the underlying population dynamics, genetics, and interactions of the composite species. In the single species context, theoretical models have simplified the study of adaptation to genotype/phenotype fitness, however complex eco-evolutionary dynamics in multi-species communities have challenged researchers. For example, in microbial and virus-immune response ecosystems, a dynamic fitness landscape determines whether pathogen strains can gain several resistance mutations. This project aims to bridge ecosystem dynamics with evolutionary genetics by analyzing ecological models evolving on fitness landscapes and developing a computational platform for incorporating phylogenetics. The advances can inform vaccines and therapies which prevent pathogen resistance against multiple immune responses or drugs. This research will engage undergraduate and graduate students, providing interdisciplinary training in computational and mathematical biology.

Recent work has sought to understand assembly of interacting species in ecosystem models. However, the overwhelming number of species combinations and connecting the models to evolution have challenged researchers, especially in higher dimensional systems. This project aims to address this gap by looking through an evolutionary genetics lens, representing species variants as binary sequences which encode ecological interactions and fitness landscapes. First, persistence and stability of equilibria in models of ecological networks will be analyzed and linked to epistasis (non-additivity) in underlying fitness landscapes, facilitating simplifying rules for ecosystem evolution. Predator-prey and consumer-resource networks pertaining to viral evolution, microbiomes and antibiotic resistance, along with applications to immunotherapy and treatments, will be considered. Next, the PI will construct a flexible computational method for jointly simulating eco-evolutionary trajectories and phylogenetic trees, which can validate the theoretical results, and confront both genetic and population dynamic data. The work will involve interdisciplinary collaboration into how fitness landscapes shape ecological network evolution for HIV-immune dynamics, and microbial resistance to antibiotics and phage infection. Through dynamical systems, stochastic simulation, combinatoric and computational analysis, techniques will be developed for connecting population dynamics and evolutionary genetics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2338630","CAREER: Multiscale Model for Cell Morphogenesis and Tissue Development in Plant Leaves","DMS","PLANT FUNGAL & MICROB DEV MECH, MATHEMATICAL BIOLOGY","07/01/2024","02/23/2024","Weitao Chen","CA","University of California-Riverside","Continuing Grant","Amina Eladdadi","06/30/2029","$185,464.00","","weitaoc@ucr.edu","200 UNIVERSTY OFC BUILDING","RIVERSIDE","CA","925210001","9518275535","MPS","111800, 733400","068Z, 1045, 8038","$0.00","This study will improve our understanding about general mechanisms involved in cell morphogenesis. Epidermal cells in plant leaves, especially pavement cells (PCs), exhibit interdigitated puzzle shapes. Shape formation of PCs serves as an ideal model to understand principles governing cell morphogenesis and tissue growth in developmental biology. During the development, PCs change from small rounded polygonal shapes into large interdigitated puzzle shapes, under the regulation of the extracellular plant hormone and multiple key molecules accumulated at the plasma membrane (PM). This developmental process also involves reorganization of cytoskeletal components and dynamic cell-to-cell communication. The multiscale mathematical model proposed in this research will have a broad range of applications from tissue engineering to biomanufacturing and biotechnology. The PI will develop a satellite undergraduate research program based on University of California, Riverside (UCR), a Hispanic-serving institution with many first generation college students. The program will also recruit students from California State Universities and high schools in local public school district. Research symposia and summer research programs will be organized through the coordination with department of mathematics, Association of Women in Mathematics at UCR Chapter, Interdisciplinary Center for Quantitative Modeling in Biology at UCR, and nearby colleges to promote public awareness on research and career paths in mathematical biology.

The morphogenesis of PCs is a complex process. During the early stage, extracellular hormone induces nanoclustering on the PM of individual cells to initiate cell polarization. It is followed by nonhomogeneous mechanical forces exerted along cell wall and a subcellular signaling gradient to regulate cell-cell interaction. Stable cell polarization, further the interdigitated jigsaw cell shapes, will be established under the regulations between the nanoclustering signals and structural components in the same cell and regulations of Rho GTPase signals between neighboring cells. Different hypotheses have been proposed for the mechanism underlying the PC morphogenesis, while most of them focus on either chemical signals or mechanical properties in PCs. The proposed study will test new hypotheses that include both the chemical signaling network and mechanical properties, as well as interactions between them, and therefore provide novel insights into the fundamental principles of cell shape formation and tissue development. This project will develop a multiscale model using the local level set method to incorporate both chemical signals and mechanical properties in a multicellular environment to test different hypotheses on the shape formation of PCs. Machine learning techniques and experimental data will be used in the modeling selection, parameter estimation and model calibration.

This CAREER project is jointly funded by the Mathematical Biology Program at the Division of Mathematical Science and the Developmental Systems Cluster at the Division of Integrative Organismal Systems in the Directorate for Biological Sciences.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2339241","CAREER: Learning stochastic spatiotemporal dynamics in single-molecule genetics","DMS","Cellular Dynamics and Function, STATISTICS, MATHEMATICAL BIOLOGY","07/01/2024","01/29/2024","Christopher Miles","CA","University of California-Irvine","Continuing Grant","Amina Eladdadi","06/30/2029","$239,517.00","","cemiles@uci.edu","160 ALDRICH HALL","IRVINE","CA","926970001","9498247295","MPS","111400, 126900, 733400","068Z, 079Z, 1045, 7465, 8038","$0.00","The ability to measure which genes are expressed in cells has revolutionized our understanding of biological systems. Discoveries range from pinpointing what makes different cell types unique (e.g., a skin vs. brain cell) to how diseases emerge from genetic mutations. This gene expression data is now a ubiquitously used tool in every cell biologist?s toolbox. However, the mathematical theories for reliably extracting insight from this data have lagged behind the amazing progress of the techniques for harvesting it. This CAREER project will develop key theoretical foundations for analyzing imaging data of gene expression. The advances span theory to practice, including developing mathematical models and machine-learning approaches that will be used with data from experimental collaborators. Altogether, the project aims to create a new gold standard of techniques in studying spatial imaging data of gene expression and enable revelation of new biological and biomedical insights. In addition, this proposed research will incorporate interdisciplinary graduate students and local community college undergraduates to train the next generation of scientists in the ever-evolving intersection of data science, biology, and mathematics. Alongside research activities, the project will create mentorship networks for supporting first-generation student scientists in pursuit of diversifying the STEM workforce.

The supported research is a comprehensive program for studying single-molecule gene expression spatial patterns through the lens of stochastic reaction-diffusion models. The key aim is to generalize mathematical connections between these models and their observation as spatial point processes. The new theory will incorporate factors necessary to describe spatial gene expression at subcellular and multicellular scales including various reactions, spatial movements, and geometric effects. This project will also establish the statistical theory of inference on the resulting inverse problem of inferring stochastic rates from only snapshots of individual particle positions. Investigations into parameter identifiability, optimal experimental design, and model selection will ensure robust and reliable inference. In complement to the developed theory, this project will implement and benchmark cutting-edge approaches for efficiently performing large-scale statistical inference, including variational Bayesian Monte Carlo and physics-informed neural networks. The culmination of this work will be packaged into open-source software that infers interpretable biophysical parameters from multi-gene tissue-scale datasets.

This CAREER Award is co-funded by the Mathematical Biology and Statistics Programs at the Division of Mathematical Sciences and the Cellular Dynamics & Function Cluster in the Division of Molecular & Cellular Biosciences, BIO Directorate.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2339000","CAREER: Dynamics and harvesting of stochastic populations","DMS","MATHEMATICAL BIOLOGY","07/01/2024","01/10/2024","Alexandru Hening","TX","Texas A&M University","Continuing Grant","Zhilan Feng","06/30/2029","$45,704.00","","ahening@tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","733400","068Z, 1045","$0.00","Environmental fluctuations have been shown to drive populations extinct, facilitate persistence, reverse competitive exclusion, change genetic diversity, and modify the spread of infectious diseases. It is important to study the interplay between environmental fluctuations, both deterministic and random, and the persistence of interacting species. Developing a rigorous mathematical theory for coexistence, in conjunction with data-driven applications, will help theoretical ecologists pinpoint how harvesting and periodic or random environmental fluctuations affect the long term dynamics of ecological communities. Global climate change models predict increasing temporal variability in temperature, precipitation and storms in the next century. The research project will provide much-needed theoretical underpinning for this fast-moving area. The application related to the harvesting of marine animals will be key for conservation and management of vulnerable or endangered species. Questions around optimal control of stochastic models are vital in today's world where there are multiple global crises in a changing environment as well as species loss. Ecologists and evolutionary biologists invoke stochasticity as a key determinant of everything from population genetics to extinction risk. But the exposure that scientists from such disciplines actually get to the mathematical concepts underpinning stochastic processes is incomplete. An integral component of the educational objectives will be the organization of a summer school at the interface of biology and stochastics targeted to advanced undergraduate and graduate students from mathematics and biology.

In order to have realistic models for the coexistence of species it is important to incorporate both periodic and random environmental fluctuations. Connecting ideas from dynamical systems and stochastic processes, it will be possible to show that the long-term dynamics is determined by the invasion rates (Lyapunov exponents) of the periodic measures living on the boundary of the state space. The developed ideas will then be used to look at non-stationary community theory where the long term behavior of the system can not be described by an equilibrium, an attractor, or a stationary distribution. An important question from conservation biology is how to harvest a given population in order to maximize the yield while not driving the population extinct. While there are a few results for single-species systems, little is known in the significantly more realistic setting of interacting species. By using a combination of novel approaches from stochastic control and Markov chain approximation methods one can analyze multi-species harvesting problems and then apply the results in order to gain insight for important real-life applications from fishery management.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2344576","Risk Factor Analysis and Dynamic Response for Epidemics in Heterogeneous Populations","DMS","Human Networks & Data Sci Res, MATHEMATICAL BIOLOGY","09/01/2024","02/14/2024","Thomas Barthel","NC","Duke University","Continuing Grant","Zhilan Feng","08/31/2027","$183,131.00","James Moody, Charles Nunn","barthel@phy.duke.edu","2200 W MAIN ST","DURHAM","NC","277054640","9196843030","MPS","147Y00, 733400","068Z","$0.00","In today's highly connected world, the prevention, prediction, and control of epidemics is of paramount importance for global health, economic productivity, and geopolitical stability. Numerous infectious disease outbreaks over the past two decades have demonstrated the need for epidemiological modeling. They also revealed shortcomings of existing scientific techniques to accurately predict epidemic dynamics and to devise effective control strategies. This project will establish a new efficient simulation method that makes it possible to assess rare but highly consequential events. It will be used to identify decisive risk factors concerning the fabric of virus-spreading interactions that can facilitate large epidemic outbreaks. A well-documented example are superspreading events that played an important role in the COVID-19 pandemic. The investigations will be focused on models for diseases similar to COVID-19 and HIV as archetypal cases. The improved understanding and models of epidemiological processes will be used to devise and analyze efficient preventive strategies with the goal of providing more reliable guidance for the general public and health-policy decision makers, saving lives and resources.

Traditionally, the dynamics of infectious diseases are studied on the basis of deterministic compartmental models, where the population is divided into large groups, and deterministic differential equations for the group sizes are employed to investigate disease dynamics. Classical examples are the deterministic SIR and SIS models. This is a strong simplification of reality that ignores to a large extent the heterogeneity in contact patterns and biomedically relevant attributes across the population as well as the stochastic nature of infection processes. Both have a decisive impact on the dynamics at the early stages of epidemic outbreaks and need to be incorporated to enable reliable predictions. Markov-chain Monte Carlo methods can sample more realistic stochastic agent-based dynamics, but cannot efficiently assess the preconditions leading to rare consequential events. The project will address this challenge with a new numerical technique that allows one to efficiently sample important but rare epidemic trajectories of realistic models under suitable constraints. The research will renew attention on the crucial role of rare events in the genesis of large outbreaks, including combinations of bottlenecks in contact networks and the stochastic nature of the disease dynamics. Risk-factor analysis based on the new method will provide answers to cutting-edge questions in disease diffusion concerning outbreak preconditions, information flow, and control strategies. This approach will open new avenues for research on the prevention and control of epidemics.

This project is jointly funded by the Mathematical Biology program of the Division of Mathematical Sciences (DMS) in the Directorate for Mathematical and Physical Sciences (MPS) and the Human Networks and Data Science program (HNDS) of the Division of Behavioral and Cognitive Sciences (BCS) in the Directorate for Social, Behavioral and Economic Sciences (SBE).

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2428961","Characterization and Prediction of Viral Capsid Geometries","DMS","MATHEMATICAL BIOLOGY","02/01/2024","05/30/2024","Antoni Luque","FL","University of Miami","Continuing Grant","Zhilan Feng","08/31/2024","$22,114.00","","axl4306@miami.edu","1320 SOUTH DIXIE HIGHWAY STE 650","CORAL GABLES","FL","331462919","3052843924","MPS","733400","","$0.00","Viruses are the most abundant biological entity on the planet and play a crucial role in the evolution of organisms and the biogeochemistry of Earth. Closely related viruses, however, can have very dissimilar genomes, complicating integration of knowledge acquired from the study of independent viruses, and limiting prediction of the characteristics and potential threats of emerging viruses. Viruses, however, conserve a few structural properties that could help circumvent this problem. Most viruses store their infective genetic material in a protein shell called a capsid. The capsid self-assembles from multiple copies of the same (or similar) proteins, and most capsids display icosahedral symmetry. This architecture optimizes the interaction of proteins and the volume available to store the viral genetic information. This research project hypothesizes that viruses have evolved a limited set of replication strategies to specialize and exploit the reduced number of geometrical templates capable of forming icosahedral capsids. This, in turn, may have constrained the number of three-dimensional configurations adopted by capsid proteins, providing a mechanistic rationale for the existence of viral structural lineages. This hypothesis will be tested by analyzing and comparing hundreds of viruses from multiple different viral families using novel mathematical methods. Confirming this hypothesis will offer a quantitative framework to study viral evolution and open the door to design of generic antiviral strategies targeting viruses in the same structural lineage.

Only ten protein folds have been identified among major capsid proteins of viruses that form icosahedral capsids. These folds define viral lineages that group viruses that can be genetically unrelated and infect hosts from different domains of life. This limited number of folds contrasts with the vast genetic diversity of viruses. The existence of these folds across the virosphere, however, remains unknown. Here, it is hypothesized that there is a direct relationship between the viral replication strategy of each viral lineage, the icosahedral lattice of the capsid, and the fold of capsid proteins. The hypothesis will be tested by developing a database that will include the viral replication, protein fold, and capsid lattice of five hundred viruses that have been reconstructed at high or medium molecular resolution. Voronoi tessellations and protein-protein interaction lattices will be obtained to identify computationally the icosahedral lattice associated to each virus. Additionally, molecular measurements of the reconstructed capsids will be obtained to establish allometric relationships for at least one viral lineage, facilitating the prediction of icosahedral capsid properties from genomic information. The new icosahedral framework will be also extended to obtain new sets of elongated capsids, which represent the second most abundant type of capsid. The methods will be disseminated online for use by viral structure researchers.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2327844","IHBEM: Using socioeconomic, behavioral and environmental data to understand disease dynamics: exploring COVID-19 outcomes in Oklahoma","DMS","MATHEMATICAL BIOLOGY, MSPA-INTERDISCIPLINARY","01/01/2024","08/23/2023","Patrick Stephens","OK","Oklahoma State University","Continuing Grant","Zhilan Feng","12/31/2026","$425,713.00","Lucas Stolerman, Juwon Hwang, Tao Hu, Rebecca Kaplan","patrick.stephens@okstate.edu","401 WHITEHURST HALL","STILLWATER","OK","740781031","4057449995","MPS","733400, 745400","068Z, 079Z, 9102, 9150, 9179","$0.00","One of the most critical modern challenges is to better understand the where, why and how oflarge disease outbreak occurrence. Research shows that the frequency of large disease outbreaks is increasing over time globally, and yet differences in outcomes remain poorly understood. This research will explore the factors that drove variation in COVID-19 outcomes across the counties and metropolitan areas of Oklahoma, particularly which areas had more or fewer cases than would be expected based on their overall population size. The investigators will look at both environmental factors, such as weather patterns and air quality, and socioeconomic factors such as numbers of doctors and differences in the proportion of individuals that were willing to be vaccinated. The investigators will also conduct surveys of individual across the state to try and better understand why people made the healthcare choices that they did and how behavior drove differences in outcomes. Understanding all of these factors requires a team with diverse expertise. Traditionally, most mathematical and quantitative models for disease dynamics have been developed and studied by mathematicians, ecologists, and computer scientists. However, understanding differences in attitudes towards health care measures and how they originate is more the purview of social scientists and historians. By building a team of collaborators spanning all of these disciplines, the research team will be able to build a more complete picture of COVID-19 outcomes in Oklahoma. This will in turn suggest what actions may be most effective to try and best mitigate the effects of both COVID and other large-scale disease events in the future. The final product of this work will include a new data repository and a public-facing intelligent epidemiological modeling platform powered by Jupyter Notebooks. The project will also provide outreach and training, including to students from underrepresented groups.

Increases in outbreak frequency seem to be related to globalization and other human activities. Yet the effects of most human behavioral, social and economic factors on outbreak risk are rarely quantified. Relevant social factors can be hard to measure, often needing specialists to generate and interpret data. However social scientists with expertise to do so are rarely trained in mathematical modelling of disease dynamics. To address these challenges, the investigators will focus on developing data sources and mathematical models that can be used to explore COVID-19 outcomes in Oklahoma. The project will be a true collaboration between social scientists and experts in modelling infectious diseases. Oklahoma is understudied, and is spatially heterogeneous such that models of disease dynamics in Oklahoma are likely to be generalizable to many other regions of the US. The Investigators will generate protocols for standardizing existing data on behavioral and socioeconomic factors as well as develop new data sources. The team will develop statistical models of past outbreaks, and mathematical models reflecting factors shown to have driven COVID-19 dynamics empirically. The latter work will demonstrate how baseline SIR-like models can be modified to reflect human behavioral factors. The Investigators will also contrast the performance of models based on existing data on socioeconomic factors with models incorporating new survey data on variation in behaviors and attitudes related to primary and secondary prevention. The code and datasets to be generated will be made freely available and searchable in an intelligent epidemiological modeling framework, which will enable other researchers to easily iterate on them.

This project is jointly funded by the Division of Mathematical Sciences (DMS) in the Directorate of Mathematical and Physical Sciences (MPS) and the Division of Social and Economic Sciences (SES) in the Directorate of Social, Behavioral and Economic Sciences (SBE).

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2428961","Characterization and Prediction of Viral Capsid Geometries","DMS","MATHEMATICAL BIOLOGY","02/01/2024","05/30/2024","Antoni Luque","FL","University of Miami","Continuing Grant","Zhilan Feng","08/31/2024","$22,114.00","","axl4306@miami.edu","1320 SOUTH DIXIE HIGHWAY STE 650","CORAL GABLES","FL","331462919","3052843924","MPS","733400","","$0.00","Viruses are the most abundant biological entity on the planet and play a crucial role in the evolution of organisms and the biogeochemistry of Earth. Closely related viruses, however, can have very dissimilar genomes, complicating integration of knowledge acquired from the study of independent viruses, and limiting prediction of the characteristics and potential threats of emerging viruses. Viruses, however, conserve a few structural properties that could help circumvent this problem. Most viruses store their infective genetic material in a protein shell called a capsid. The capsid self-assembles from multiple copies of the same (or similar) proteins, and most capsids display icosahedral symmetry. This architecture optimizes the interaction of proteins and the volume available to store the viral genetic information. This research project hypothesizes that viruses have evolved a limited set of replication strategies to specialize and exploit the reduced number of geometrical templates capable of forming icosahedral capsids. This, in turn, may have constrained the number of three-dimensional configurations adopted by capsid proteins, providing a mechanistic rationale for the existence of viral structural lineages. This hypothesis will be tested by analyzing and comparing hundreds of viruses from multiple different viral families using novel mathematical methods. Confirming this hypothesis will offer a quantitative framework to study viral evolution and open the door to design of generic antiviral strategies targeting viruses in the same structural lineage.

Only ten protein folds have been identified among major capsid proteins of viruses that form icosahedral capsids. These folds define viral lineages that group viruses that can be genetically unrelated and infect hosts from different domains of life. This limited number of folds contrasts with the vast genetic diversity of viruses. The existence of these folds across the virosphere, however, remains unknown. Here, it is hypothesized that there is a direct relationship between the viral replication strategy of each viral lineage, the icosahedral lattice of the capsid, and the fold of capsid proteins. The hypothesis will be tested by developing a database that will include the viral replication, protein fold, and capsid lattice of five hundred viruses that have been reconstructed at high or medium molecular resolution. Voronoi tessellations and protein-protein interaction lattices will be obtained to identify computationally the icosahedral lattice associated to each virus. Additionally, molecular measurements of the reconstructed capsids will be obtained to establish allometric relationships for at least one viral lineage, facilitating the prediction of icosahedral capsid properties from genomic information. The new icosahedral framework will be also extended to obtain new sets of elongated capsids, which represent the second most abundant type of capsid. The methods will be disseminated online for use by viral structure researchers.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2330970","Trait-shift induced interaction modification: How individual variation affects ecosystem stability","DMS","Population & Community Ecology, MATHEMATICAL BIOLOGY","05/01/2024","02/01/2024","BingKan Xue","FL","University of Florida","Standard Grant","Amina Eladdadi","04/30/2027","$561,268.00","Robert Holt, Mathew Leibold","b.xue@ufl.edu","1523 UNION RD RM 207","GAINESVILLE","FL","326111941","3523923516","MPS","112800, 733400","068Z, 124Z","$0.00","Individual organisms of the same species can exhibit substantial variation in traits that are important for their interaction with the environment and other species. The distribution of such variable traits within a species can shift over time. For example, behavioral traits can change quickly in response to environmental change or species interactions. The dynamic shift of trait distribution within a species can modify the interaction patterns among species and ultimately affect the stability of ecosystems. However, the prevalence and significance of such effects have not been evaluated systematically. This research project aims to fill in the gap by integrating theoretical and empirical approaches. A mathematical framework will be developed to classify different types of interaction modification and identify conditions that would destabilize ecosystems. Additionally, a comprehensive survey of empirical studies will be conducted to assess the level of evidence for the various types of interaction modification identified above and provide criteria for evaluating past and future case studies. This project will train young researchers in the interdisciplinary area between mathematics and ecology to address important environmental and ecological problems facing the next generation. In addition, educational kits and programs will be designed to promote teaching of important ecological concepts and engage underrepresented groups in K-12 schools.

Intraspecific trait variation has been increasingly recognized as an important factor in determining ecological and evolutionary dynamics. Although some work has examined how the variation of heritable traits affects eco-evolutionary dynamics, non-heritable variation caused by phenotypic plasticity, developmental differences, or species interactions has received less consideration. Ecosystems have traditionally been studied as dynamical systems with fixed interaction strengths, but these interaction strengths will no longer be constant if the trait distributions can shift within short timescales. Such ?trait-shift induced interaction modification? (TSIIM) can lead to higher-order interactions among species, causing species extinction or coexistence that are otherwise unexpected. This project will develop a theoretical framework for studying TSIIM by generalizing traditional dynamical systems to incorporate intraspecific trait variation and categorizing these systems into different network motifs. The effect on large ecosystems will be studied using a disordered systems approach augmented by the new motifs. Meta-analysis of these motifs using empirical studies will provide insight on the mechanisms by which higher-order interactions arise from TSIIM, prompting experimental searches for such phenomena and their consequences.


This project is jointly funded by the Mathematical Biology Program at the Division of Mathematical Sciences and the Population and Community Ecology Cluster in the Division of Environmental Biology at the Directorate for Biological Sciences.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2327892","Collaborative Research: RUI: Topological methods for analyzing shifting patterns and population collapse","DMS","Population & Community Ecology, MATHEMATICAL BIOLOGY, EPSCoR Co-Funding","02/01/2024","01/25/2024","Laura Storch","ME","Bates College","Standard Grant","Zhilan Feng","01/31/2027","$169,439.00","","lstorch@bates.edu","2 ANDREWS ROAD","LEWISTON","ME","042406030","2077868375","MPS","112800, 733400, 915000","9150, 9229","$0.00","Profound and irreversible changes in ecosystems, such as population collapse, are occurring globally due to climate change, habitat destruction, and overuse of natural resources, and are only expected to become more frequent in the future. To prevent an impending collapse, we must recognize the early warning signs. This is particularly challenging in ecological systems due to their naturally complex behavior in both space and time, as well as noisy and/or poorly resolved data. In this project, the investigators will use a novel approach for early detection of impending population collapse, and apply the methodology to spatially distributed populations, for example, a grassland. They utilize a method called computational topology, which can quantify features of a population distribution pattern, such as the level of patchiness in the pattern. In previous work, the investigators used a spatial population model to quantify the changes in a population distribution pattern that occurred as the population went extinct and observed a ""topological route to extinction"". In this project, the investigators will develop and extend the methodology for use in stochastic population models and real-world data sets, which are expected to contain high levels of noise and/or missing/corrupted data. The developed methodology will serve as an additional tool for the prediction of impending population collapse. This tool can then be used by conservation biologists and natural resource managers in order to assist in preserving vulnerable species and ecosystems. The project also supports undergraduate research, and includes recruitment efforts directed at students from underrepresented groups.

In previous work on data generated by a deterministic population model, the investigators measured changes in topological features (via cubical homology) of population distribution patterns en route to extinction, and observed clear topological signatures of impending collapse. Results with the deterministic model serve as a proof of concept, but in this project, the investigators will study dynamical changes in stochastic population models and real ecological data sets. Transitioning from deterministic to stochastic systems will require substantial development of the methodology, and will require the use of more sophisticated tools, e.g., multiparameter persistent homology. The developed methodology must be able to detect signal in noisy data, corrupted data, missing data, and data that is sparse in space and/or time. Because the topological approach can distinguish fine-scale stochastic noise from large-scale deterministic spatial patterns, it is a promising tool for the analysis of noisy ecological data, and preliminary work using multiparameter persistence shows that it is capable of recovering ""true? dynamical signal (a population distribution pattern) from noise.

This project is jointly funded by the Mathematical Biology program of the Division of Mathematical Sciences (DMS) in the Directorate for Mathematical and Physical Sciences (MPS), the Established Program to Stimulate Competitive Research (EPSCoR), and the Population and Community Ecology Cluster (PEC) of the Division of Environmental Biology (DEB) in the Directorate for Biological Sciences (BIO).

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2327893","Collaborative Research: RUI: Topological methods for analyzing shifting patterns and population collapse","DMS","Population & Community Ecology, MATHEMATICAL BIOLOGY","02/01/2024","01/25/2024","Sarah Day","VA","College of William and Mary","Standard Grant","Zhilan Feng","01/31/2027","$192,542.00","","sday@math.wm.edu","1314 S MOUNT VERNON AVE","WILLIAMSBURG","VA","231852817","7572213965","MPS","112800, 733400","068Z, 9150, 9229","$0.00","Profound and irreversible changes in ecosystems, such as population collapse, are occurring globally due to climate change, habitat destruction, and overuse of natural resources, and are only expected to become more frequent in the future. To prevent an impending collapse, we must recognize the early warning signs. This is particularly challenging in ecological systems due to their naturally complex behavior in both space and time, as well as noisy and/or poorly resolved data. In this project, the investigators will use a novel approach for early detection of impending population collapse, and apply the methodology to spatially distributed populations, for example, a grassland. They utilize a method called computational topology, which can quantify features of a population distribution pattern, such as the level of patchiness in the pattern. In previous work, the investigators used a spatial population model to quantify the changes in a population distribution pattern that occurred as the population went extinct and observed a ""topological route to extinction"". In this project, the investigators will develop and extend the methodology for use in stochastic population models and real-world data sets, which are expected to contain high levels of noise and/or missing/corrupted data. The developed methodology will serve as an additional tool for the prediction of impending population collapse. This tool can then be used by conservation biologists and natural resource managers in order to assist in preserving vulnerable species and ecosystems. The project also supports undergraduate research, and includes recruitment efforts directed at students from underrepresented groups.

In previous work on data generated by a deterministic population model, the investigators measured changes in topological features (via cubical homology) of population distribution patterns en route to extinction, and observed clear topological signatures of impending collapse. Results with the deterministic model serve as a proof of concept, but in this project, the investigators will study dynamical changes in stochastic population models and real ecological data sets. Transitioning from deterministic to stochastic systems will require substantial development of the methodology, and will require the use of more sophisticated tools, e.g., multiparameter persistent homology. The developed methodology must be able to detect signal in noisy data, corrupted data, missing data, and data that is sparse in space and/or time. Because the topological approach can distinguish fine-scale stochastic noise from large-scale deterministic spatial patterns, it is a promising tool for the analysis of noisy ecological data, and preliminary work using multiparameter persistence shows that it is capable of recovering ""true? dynamical signal (a population distribution pattern) from noise.

This project is jointly funded by the Mathematical Biology program of the Division of Mathematical Sciences (DMS) in the Directorate for Mathematical and Physical Sciences (MPS), the Established Program to Stimulate Competitive Research (EPSCoR), and the Population and Community Ecology Cluster (PEC) of the Division of Environmental Biology (DEB) in the Directorate for Biological Sciences (BIO).

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." diff --git a/Statistics/Awards-Statistics-2024.csv b/Statistics/Awards-Statistics-2024.csv index 4d2703e..31f3d13 100644 --- a/Statistics/Awards-Statistics-2024.csv +++ b/Statistics/Awards-Statistics-2024.csv @@ -1,7 +1,8 @@ "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract" +"2434559","NSF-SNSF: Functional data analysis for complex systems","DMS","STATISTICS","09/01/2024","08/19/2024","Sreekalyani Bhamidi","NC","University of North Carolina at Chapel Hill","Continuing Grant","Yong Zeng","08/31/2028","$49,414.00","","bhamidi@email.unc.edu","104 AIRPORT DR STE 2200","CHAPEL HILL","NC","275995023","9199663411","MPS","126900","022Z, 075Z, 079Z, 129Z, 5950","$0.00","Networks play a major role in many disciplines, both as the primary medium of interest, for instance, the flow of (mis)-information in social networks, or unobserved relationships describing developmental trajectories in cells in individuals, or as a fundamental ingredient in representing high dimensional data in sophisticated multi-step machine learning pipelines. While tremendous advancements have been made in the formulation and application of network-driven techniques on data, the main aim of this project is to provide a theoretical understanding of such models and the accuracy of ensuing scientific conclusions. The project will focus on two major sub-domains, (1) understanding multilayer network data, e.g., network-valued data on a single individual over multiple time points or multi-population data points across different tasks as well as understanding the time evolution of such systems and (2) developing mathematical techniques to understand properties of a major class of techniques used to analyze high dimensional data, namely Gaussian graphical models. This project also provides research training opportunities for graduate students.

The project is focused on two major areas of statistical methodology related to functional data analysis for complex systems: (I) Optimal transport for multilayer networks and trajectory inference for complex systems and (II) Continuum scaling limits in Graphical models. In the first domain, the PIs will develop statistically principled techniques for network summarization, clustering, and extraction of principle directions of variation building on Gaussian process optimal transport techniques from functional data analysis, and specifically the representation of Procrustes metrics on covariance operators via the Wasserstein distance between corresponding Gaussian processes. Related to this first domain, motivated by single-cell RNA-seq and network neuroscience, the project will develop mathematical techniques to understand optimal transport-based methods for registration (time synchronization) and supervised learning tasks, including network clustering, after quotienting out the underlying developmental trajectory. Next, driven by areas such as gene-expression data from cancer genomics, the main goal for the second theme is the study of high-dimensional data with underlying dependency structures modulated by a latent network connecting the features. Mathematical techniques that will be developed include (a) Thresholding pipelines from covariance and correlation matrices and local weak convergence of associated objects to limit infinite structures and corresponding implications for thresholding schemes; (b) Hierarchical Representation learning for complex systems and their connection to convergence to continuum scaling limits via connections between linkage clustering and thresholding; (c) Structured alternatives, penalized estimation and limiting distributions of random adjacency matrices including localization phenomena for eigenvectors and their use in hub-detection.

This collaborative U.S.-Swiss project is supported by the U.S. National Science Foundation (NSF) and the Swiss National Science Foundation (SNSF), where NSF funds the U.S. investigator and SNSF funds the partners in Switzerland.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413828","Fundamental Limits of High-Dimensional Statistical Estimation","DMS","STATISTICS","09/01/2024","08/15/2024","Cynthia Rush","NY","Columbia University","Standard Grant","Tapabrata Maiti","08/31/2026","$117,910.00","","cynthia.rush@columbia.edu","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","126900","","$0.00","Many challenges facing statisticians today are related to making decisions based on and drawing conclusions from complex datasets that are quite different from datasets studied before the existence of modern computers. For instance, data collected in fields like genetics, astronomy, and finance are now often high-dimensional, unstructured, multimodal, and extremely large. Therefore, a core challenge facing statisticians in today's world is to develop and analyze methods for learning from data under the restrictions that the procedures remain computationally efficient in the face of such modern complexities and perform close to the theoretically optimal performance limits when enough data is available. In particular, with the increasing societal value of massive data collection and processing, we must build statistical estimation systems and procedures that are energy-efficient; hence, sustainable. This project will lead to increases in the computational efficiencies of algorithms, and conceptually, will be crucial to improve estimation quality from a reduced number of measurements in large-scale problems, while simultaneously creating new applications of such methods in wireless communications. Beyond the research activities, this project includes specific initiatives to develop the research arm of a program to identify, support, and help build the academic portfolios of undergraduate students in the New York City tri-state area who aspire to be researchers in statistics and data science and who are from historically underrepresented populations in these disciplines, as well as to formalize and expand undergraduate research opportunities for local students with an emphasis on training a new generation of statisticians and data scientists with interdisciplinary skill sets and research interests.

This project will tackle challenges caused by modern, complex data by investigating the following questions: (A) Exactly how well do modern statistical procedures perform when datasets are growing rapidly? (B) Given a complex statistics or machine learning task, how much data, or information, is needed to solve it? How much data is needed if we impose computational constraints on algorithm efficiency? (C) How can recent advances in understanding high-dimensional statistics be used for engineering systems design? We will address three lines of inquiry related to these challenges. First, as a community, we have an incomplete understanding of how standard statistical estimation methods perform in high-dimensional settings, where the number of parameters grows with the number of data points. To address this, the proposed work will provide rigorous theoretical guarantees for estimation performance for large classes of penalized estimators for high-dimensional (generalized) linear models. Secondly, while we have a fairly complete picture of fundamental limits after which no algorithm will be able to successfully extract signal from noise in statistical estimation, detection, and inference, we have a much more limited understanding of such fundamental limits when constraints are placed on algorithm efficiency. Proposed work will establish such computational limits for various modern procedures under complex, but relevant, modeling assumptions that allow the problem structure to change as dimensions grow. Finally, the key challenge in wireless communication is to devise coding schemes for transmitting information reliably from a sender to a receiver through a noisy channel that are computationally efficient, have a low probability of decoding error, and allow for data rates close to the information-theoretically optimal value, the channel capacity. This project will design new algorithms for this kind of communication by leveraging ideas from high-dimensional statistical estimation procedures where we know efficient algorithms can perform close to information theoretic limits.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2432249","Conference: NISS 2024 Writing Workshop for Jr Researchers","DMS","STATISTICS","08/15/2024","08/16/2024","Piaomu Liu","NC","National Institute of Statistical Sciences","Standard Grant","Tapabrata Maiti","08/31/2026","$19,000.00","","pliu@bentley.edu","19 TW ALEXANDER DR","DURHAM","NC","277090152","9196859300","MPS","126900","7556","$0.00","The National Institute of Statistical Sciences (NISS) Writing Workshop for Junior Researchers in 2024 will be a hybrid event, held online on two Fridays in July and at the Joint Statistical Meetings on August 4, 2024, in Portland, OR. The workshop focuses on enhancing junior statistical scientists? technical writing abilities for various professional contexts. It will cover targeting publications, grant writing intricacies, manuscript revision, collaboration, ethics, reproducibility, and addressing challenges faced by non-native English speakers. Additionally, it will explore the role of AI, including an introduction to ChatGPT, and feature a panel discussing AI?s influence on writing and statistics.

The NISS Writing Workshop for Junior Researchers has been nurturing top statistical writers for over a decade, offering early-career connections with leading professionals. Recognizing the essential yet often overlooked role of writing in statistics, the workshop will be hybrid to expand its reach. It will cover technical writing, publication strategies, peer review navigation, collaborative writing, and funding insights, along with reproducibility and ethics. The JSM in-person session will delve into AI?s impact on the field, featuring a ChatGPT tutorial and a panel discussion. Thirty five junior researchers from statistics and related fields will receive personalized mentorship from experienced mentors, including former journal editors and NSF and NIH directors. Submissions are due by June 30. The workshop website is available here: https://www.niss.org/events/writing-workshop-junior-researchers-2024.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2415067","Collaborative Research: New Regression Models and Methods for Studying Multiple Categorical Responses","DMS","STATISTICS","01/15/2024","01/26/2024","Aaron Molstad","MN","University of Minnesota-Twin Cities","Continuing Grant","Yong Zeng","08/31/2025","$67,380.00","","amolstad@umn.edu","200 OAK ST SE","MINNEAPOLIS","MN","554552009","6126245599","MPS","126900","079Z","$0.00","In many areas of scientific study including bioengineering, epidemiology, genomics, and neuroscience, an important task is to model the relationship between multiple categorical outcomes and a large number of predictors. In cancer research, for example, it is crucial to model whether a patient has cancer of subtype A, B, or C and high or low mortality risk given the expression of thousands of genes. However, existing statistical methods either cannot be applied, fail to capture the complex relationships between the response variables, or lead to models that are difficult to interpret and thus, yield little scientific insight. The PIs address this deficiency by developing multiple new statistical methods. For each new method, the PIs will provide theoretical justifications and fast computational algorithms. Along with graduate and undergraduate students, the PIs will also create publicly available software that will enable applications across both academia and industry.

This project aims to address a fundamental problem in multivariate categorical data analysis: how to parsimoniously model the joint probability mass function of many categorical random variables given a common set of high-dimensional predictors. The PIs will tackle this problem by using emerging technologies on tensor decompositions, dimension reduction, and both convex and non-convex optimization. The project focuses on three research directions: (1) a latent variable approach for the low-rank decomposition of a conditional probability tensor; (2) a new overlapping convex penalty for intrinsic dimension reduction in a multivariate generalized linear regression framework; and (3) a direct non-convex optimization-based approach for low-rank tensor regression utilizing explicit rank constraints on the Tucker tensor decomposition. Unlike the approach of regressing each (univariate) categorical response on the predictors separately, the new models and methods will allow practitioners to characterize the complex and often interesting dependencies between the responses.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2432249","Conference: NISS 2024 Writing Workshop for Jr Researchers","DMS","STATISTICS","08/15/2024","08/16/2024","Piaomu Liu","NC","National Institute of Statistical Sciences","Standard Grant","Tapabrata Maiti","08/31/2026","$19,000.00","","pliu@bentley.edu","19 TW ALEXANDER DR","DURHAM","NC","277090152","9196859300","MPS","126900","7556","$0.00","The National Institute of Statistical Sciences (NISS) Writing Workshop for Junior Researchers in 2024 will be a hybrid event, held online on two Fridays in July and at the Joint Statistical Meetings on August 4, 2024, in Portland, OR. The workshop focuses on enhancing junior statistical scientists? technical writing abilities for various professional contexts. It will cover targeting publications, grant writing intricacies, manuscript revision, collaboration, ethics, reproducibility, and addressing challenges faced by non-native English speakers. Additionally, it will explore the role of AI, including an introduction to ChatGPT, and feature a panel discussing AI?s influence on writing and statistics.

The NISS Writing Workshop for Junior Researchers has been nurturing top statistical writers for over a decade, offering early-career connections with leading professionals. Recognizing the essential yet often overlooked role of writing in statistics, the workshop will be hybrid to expand its reach. It will cover technical writing, publication strategies, peer review navigation, collaborative writing, and funding insights, along with reproducibility and ethics. The JSM in-person session will delve into AI?s impact on the field, featuring a ChatGPT tutorial and a panel discussion. Thirty five junior researchers from statistics and related fields will receive personalized mentorship from experienced mentors, including former journal editors and NSF and NIH directors. Submissions are due by June 30. The workshop website is available here: https://www.niss.org/events/writing-workshop-junior-researchers-2024.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2436549","Collaborative Research: FDT-BioTech: Aspects of Digital Twin Studies for Neuroimages","DMS","OFFICE OF MULTIDISCIPLINARY AC, STATISTICS, MSPA-INTERDISCIPLINARY, ","09/01/2024","08/13/2024","Snigdhansu Chatterjee","MD","University of Maryland Baltimore County","Standard Grant","Zhilan Feng","08/31/2027","$888,680.00","Karuna Joshi, Animikh Biswas","snigchat@umbc.edu","1000 HILLTOP CIR","BALTIMORE","MD","212500001","4104553140","MPS","125300, 126900, 745400, Y18200","075Z, 079Z, 8038","$0.00","Neurodegenerative diseases (for example, Alzheimer's disease, Parkinson's disease, multiple sclerosis) impact millions of people in the United States and result in hundreds of thousands of deaths. These disorders can affect people of all ages, although they are more common in older adults. Digital twin models, leveraging the exponential growth of biomedical data and artificial intelligence and data science techniques, are opening exciting avenues to obtain new insights into these diseases and revolutionize their treatment and prevention. The investigators will address multiple problems on this interface, and develop data science-driven theoretical foundations, methodological tools and algorithmic principles for several aspects of digital twin models towards better understanding of digital twins as a whole, and in particular in the context of their use in neuroscience and in prevention, treatment and better understanding of neurodegenerative diseases. They will also address the ethical, legal, and social implications of using digital twin models in the context of healthcare in general, and in studying neurodegenerative diseases using magnetic resonance-technology driven images (MRI) in particular. This research will greatly aid in the deployment of digital twins in medical and healthcare practice, and will significantly advance neuroscience and the study of neurodegenerative diseases.

The investigators will address open problems in low-dimensional manifold learning, causal pathway searches and feature discoveries and selections, and develop multiple techniques for verification, validation and uncertainty quantification of digital twins using Bayesian techniques, data assimilation, resampling, empirical likelihood methods and topological data analysis. They will also develop dynamical system models, incorporating observational image data, for computational efficiency and synthetic data generation for ethical use of artificial intelligence and digital twin technology in studying neurodegenerative diseases. Additionally, they will develop knowledge graph driven systems for use by regulatory and other healthcare monitoring agencies for de-risking and easy implementation of data-driven modern technologies. The investigators will work in conjunction with regulatory and other healthcare governing agencies towards better understanding of neurodegenerative diseases and successful deployment of data-driven technologies to mitigate suffering from such diseases. The investigators will mentor, train and teach students on various aspects of digital twins, data science and neuroscience and their interconnections, and will help build a highly skilled workforce on these topics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2436649","Conference: International Indian Statistical Association 2024 Annual Flagship Conference in India","DMS","STATISTICS","09/01/2024","08/13/2024","Saonli Basu","MN","University of Minnesota-Twin Cities","Standard Grant","Tapabrata Maiti","08/31/2025","$25,000.00","","saonli@umn.edu","200 OAK ST SE","MINNEAPOLIS","MN","554552009","6126245599","MPS","126900","7556","$0.00","This project supports a five-day international conference at the Cochin University of Science and Technology (CUSAT) in Kochi, India, from December 27 to December 31, 2024. The conference serves as the official annual meeting of the International Indian Statistical Association (IISA). The conference provides its members a unique opportunity to meet and exchange ideas among researchers, and students with a broad focus on theoretical, methodological, and applied research across various scientific domains. Attendees can expect captivating plenary sessions, special invited talks, panel discussions, and a diverse array of invited and contributed sessions. IISA and CUSAT are the primary organizers of the conference.

The conference's main objective is to bring together well-established and emerging young researchers from around the world who are actively pursuing theoretical and methodological research in statistics, data science, and their applications in various allied fields. It aims to provide a forum for leading experts and young researchers to discuss recent progress in statistical theory and data science. The conference offers a vibrant agenda, including student paper competitions, insightful presentations, and awards, complemented by enriching workshops and the esteemed Early Career Award in Statistics and Data Science (ECASDS). It strives to maintain a healthy presence of women and minorities in all these categories and of young researchers (within five years of their doctoral degrees) in invited sessions. The meeting is primarily self-funded, with revenue primarily coming from registration. The revenue generated from the registration fee will be mainly used to cover the cost of the conference. The requested budget will cover registration, partial airfare, and lodging for 20 students and 8 junior researchers to support the participation of students studying at US institutions and US-based junior researchers in the 2024 IISA conference. The official website https://www.intindstat.org/conference2024/index provides details on different activities planned during the conference.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2426173","Collaborative Research: Unlocking Complex Heterogeneity in Large Spatial-Temporal Data with Scalable Quantile Learning","DMS","STATISTICS, CDS&E","09/01/2024","08/13/2024","Lily Wang","VA","George Mason University","Continuing Grant","Tapabrata Maiti","08/31/2027","$169,371.00","","lwang41@gmu.edu","4400 UNIVERSITY DR","FAIRFAX","VA","220304422","7039932295","MPS","126900, 808400","9263","$0.00","Advancements in modern technology have exponentially increased the availability and complexity of spatial and spatiotemporal data across various fields, presenting unique challenges and opportunities. This project aims to develop scalable and efficient quantile learning techniques to unlock valuable insights from large-scale, heterogeneous spatial-temporal data, overcoming limitations in handling dynamic patterns and spatial variations while accounting for uncertainty. These new analytical techniques will have wide-ranging applications, revolutionizing our understanding of spatial and temporal variations in critical areas. For example, they can help identify communities facing disproportionate risks from environmental hazards, health crises, or crime, enabling more targeted and effective interventions. By making these techniques widely accessible through public software releases, the project will empower researchers and policymakers to leverage vast amounts of spatial-temporal data and address pressing societal issues more effectively. The project will also contribute to STEM education by engaging both undergraduate and graduate students in hands-on learning and incorporating research findings into course development.

The project will develop scalable and efficient quantile learning methodologies, algorithms, and theories to address challenges in analyzing large-scale spatial-temporal data through three main research aims. First, the investigators will introduce a flexible quantile spatial model framework that simultaneously captures spatial nonstationarity and heterogeneity via spatially varying coefficients. Second, they will develop a scalable distributed learning procedure using domain decomposition computing to efficiently handle large spatial datasets across complex domains, including a communication-efficient aggregation method for estimating constant coefficients to ensure optimal efficiency. Third, the research will expand analysis from 2D to 3D to tackle complex and heterogeneous dynamics of extremely large spatiotemporal data, introducing a class of quantile spatiotemporal models and developing a robust, scalable estimating procedure to meet substantial computational demands. These advancements will significantly impact multiple areas of statistics, including large-scale computing, inference, optimization, and nonparametric approximation theory.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria."