From 11c0021148c0f7b548e1bf1815569cf7ec2838b0 Mon Sep 17 00:00:00 2001 From: Yimin Zhong Date: Fri, 23 Aug 2024 06:38:17 +0000 Subject: [PATCH] Update Awards --- .../Awards-Algebra-and-Number-Theory-2024.csv | 5 +++-- .../Awards-Applied-Mathematics-2024.csv | 15 ++++++++------- .../Awards-Computational-Mathematics-2024.csv | 3 ++- .../Awards-Mathematical-Biology-2024.csv | 7 ++++--- 4 files changed, 17 insertions(+), 13 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 03e8254..920cb96 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 @@ -1,10 +1,12 @@ "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" +"2401279","Birational classification of varieties: connections to arithmetic and algebra","DMS","ALGEBRA,NUMBER THEORY,AND COM","09/01/2024","08/21/2024","Joseph Waldron","MI","Michigan State University","Standard Grant","James Matthew Douglass","08/31/2027","$172,000.00","","waldro51@msu.edu","426 AUDITORIUM RD RM 2","EAST LANSING","MI","488242600","5173555040","MPS","126400","","$0.00","An algebraic variety is a geometric object defined as the set of points at which a set of multivariate polynomial equations vanishes, with the most elementary examples being the conic sections. While algebraic varieties are the fundamental objects of algebraic geometry, they also appear in many other diverse fields, such as number theory and computer vision. Birational geometry aims to classify higher dimensional varieties in terms of their intrinsic properties such as curvature. Over the past few decades, there has been tremendous progress in the classification of varieties whose points take values in the complex numbers, and many of the major conjectures are now known in that context. However, there are many other situations in which the theory could apply, and much less is known about these. For example, number theorists are mainly interested in varieties whose points take values in finite fields or the integers, since the (non-)existence of these points appears in statements such as Fermat's last theorem. In this project, the PI will investigate birational geometry in these other settings. In addition, the project will provide research training opportunities for students and will support various initiatives promoting broadening participation in mathematics, with particular focus on first-generation college students.

In more detail, the project has three main research goals. The first is to investigate the moduli theory and boundedness of Fano varieties over the integers, particularly in dimension two and three. In the process, the PI will explore connection with commutative algebra and new techniques from arithmetic geometry. The second objective is to investigate the birational classification of non-commutative surfaces from the point of view of Mori theory. Finally, the PI will apply new techniques from derived algebraic geometry to investigate problems involving the purely inseparable covers which lie behind many positive characteristic pathologies.

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." "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." +"2338485","CAREER: Moduli Spaces, Fundamental Groups, and Asphericality","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","07/01/2024","02/02/2024","Nicholas Salter","IN","University of Notre Dame","Continuing Grant","Swatee Naik","06/30/2029","$67,067.00","","nsalter@nd.edu","940 GRACE HALL","NOTRE DAME","IN","465565708","5746317432","MPS","126400, 126700","1045","$0.00","This NSF CAREER award provides support for a research program at the interface of algebraic geometry and topology, as well as outreach efforts aimed at improving the quality of mathematics education in the United States. Algebraic geometry can be described as the study of systems of polynomial equations and their solutions, whereas topology is the mathematical discipline that studies notions such as ?shape? and ?space"" and develops mathematical techniques to distinguish and classify such objects. A notion of central importance in these areas is that of a ?moduli space? - this is a mathematical ?world map? that gives a complete inventory and classification of all instances of a particular mathematical object. The main research objective of the project is to better understand the structure of these spaces and to explore new phenomena, by importing techniques from neighboring areas of mathematics. While the primary aim is to advance knowledge in pure mathematics, developments from these areas have also had a long track record of successful applications in physics, data science, computer vision, and robotics. The educational component includes an outreach initiative consisting of a ?Math Circles Institute? (MCI). The purpose of the MCI is to train K-12 teachers from around the country in running the mathematical enrichment activities known as Math Circles. This annual 1-week program will pair teachers with experienced instructors to collaboratively develop new materials and methods to be brought back to their home communities. In addition, a research conference will be organized with the aim of attracting an international community of researchers and students and disseminating developments related to the research objectives of the proposal.

The overall goal of the research component is to develop new methods via topology and geometric group theory to study various moduli spaces, specifically, (1) strata of Abelian differentials and (2) families of polynomials. A major objective is to establish ?asphericality"" (vanishing of higher homotopy) of these spaces. A second objective is to develop the geometric theory of their fundamental groups. Asphericality occurs with surprising frequency in spaces coming from algebraic geometry, and often has profound consequences. Decades on, asphericality conjectures of Arnol?d, Thom, and Kontsevich?Zorich remain largely unsolved, and it has come to be regarded as a significantly challenging topic. This project?s goal is to identify promising-looking inroads. The PI has developed a method called ""Abel-Jacobi flow"" that he proposes to use to establish asphericality of some special strata of Abelian differentials. A successful resolution of this program would constitute a major advance on the Kontsevich?Zorich conjecture; other potential applications are also described. The second main focus is on families of polynomials. This includes linear systems on algebraic surfaces; a program to better understand the fundamental groups is outlined. Two families of univariate polynomials are also discussed, with an eye towards asphericality conjectures: (1) the equicritical stratification and (2) spaces of fewnomials. These are simple enough to be understood concretely, while being complex enough to require new techniques. In addition to topology, the work proposed here promises to inject new examples into geometric group theory. Many of the central objects of interest in the field (braid groups, mapping class groups, Artin groups) are intimately related to algebraic geometry. The fundamental groups of the spaces the PI studies here should be just as rich, and a major goal of the project is to bring this to fruition.

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." +"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." "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." @@ -126,4 +128,3 @@ "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." "2400553","Conference: Arithmetic quantum field theory","DMS","ALGEBRA,NUMBER THEORY,AND COM","03/01/2024","02/12/2024","Daniel Freed","MA","Harvard University","Standard Grant","Andrew Pollington","02/28/2025","$45,000.00","David Ben-Zvi","dafr@math.harvard.edu","1033 MASSACHUSETTS AVE STE 3","CAMBRIDGE","MA","021385366","6174955501","MPS","126400","7556","$0.00","The conference Arithmetic Quantum Field Theory will be held at the Harvard Center of Mathematical Sciences and Applications (CMSA) on March 25-29 2024. This will be an in-person gathering of approximately 70 researchers - graduate students, postdocs, and faculty in mathematics and physics, available in hybrid mode to an unlimited number of outside participants. A central focus of the conference - and the dedicated aim of its first day - is to encourage a high level of participation by women in math and physics. The first day is designed to encourage junior researchers to come and network, give talks in a friendly environment, and participate without concern over the precise fit of their research to the narrow theme of the workshop.

The conference Arithmetic Quantum Field Theory, and the two-month program of the same title it concludes, are aimed at catalyzing interactions between mathematicians and physicists by disseminating exciting new connections emerging between quantum field theory and algebraic number theory, and in particular between the fundamental invariants of each: partition functions and L-functions. On one hand, there has been tremendous progress in the past decade in our understanding of the algebraic structures underlying quantum field theory as expressed in terms of the geometry and topology of low-dimensional manifolds. On the other hand, the arithmetic topology dictionary provides a sturdy bridge between the topology of manifolds and the arithmetic of number fields. Thus, one can now port over quantum field theoretic ideas to number theory. The program will bring together a wide range of mathematicians and physicists working on adjacent areas to explore the emerging notion of arithmetic quantum field theory as a tool to bring quantum physics to bear on questions of interest for the theory of automorphic forms, harmonic analysis and L-functions, and conversely to explore potential geometric and physical consequences of arithmetic ideas.
The conference website is https://cmsa.fas.harvard.edu/event/aqftconf/ where recordings of the talks and notes from lectures will be made widely available.

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." -"2338485","CAREER: Moduli Spaces, Fundamental Groups, and Asphericality","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","07/01/2024","02/02/2024","Nicholas Salter","IN","University of Notre Dame","Continuing Grant","Swatee Naik","06/30/2029","$67,067.00","","nsalter@nd.edu","836 GRACE HALL","NOTRE DAME","IN","465566031","5746317432","MPS","126400, 126700","1045","$0.00","This NSF CAREER award provides support for a research program at the interface of algebraic geometry and topology, as well as outreach efforts aimed at improving the quality of mathematics education in the United States. Algebraic geometry can be described as the study of systems of polynomial equations and their solutions, whereas topology is the mathematical discipline that studies notions such as ?shape? and ?space"" and develops mathematical techniques to distinguish and classify such objects. A notion of central importance in these areas is that of a ?moduli space? - this is a mathematical ?world map? that gives a complete inventory and classification of all instances of a particular mathematical object. The main research objective of the project is to better understand the structure of these spaces and to explore new phenomena, by importing techniques from neighboring areas of mathematics. While the primary aim is to advance knowledge in pure mathematics, developments from these areas have also had a long track record of successful applications in physics, data science, computer vision, and robotics. The educational component includes an outreach initiative consisting of a ?Math Circles Institute? (MCI). The purpose of the MCI is to train K-12 teachers from around the country in running the mathematical enrichment activities known as Math Circles. This annual 1-week program will pair teachers with experienced instructors to collaboratively develop new materials and methods to be brought back to their home communities. In addition, a research conference will be organized with the aim of attracting an international community of researchers and students and disseminating developments related to the research objectives of the proposal.

The overall goal of the research component is to develop new methods via topology and geometric group theory to study various moduli spaces, specifically, (1) strata of Abelian differentials and (2) families of polynomials. A major objective is to establish ?asphericality"" (vanishing of higher homotopy) of these spaces. A second objective is to develop the geometric theory of their fundamental groups. Asphericality occurs with surprising frequency in spaces coming from algebraic geometry, and often has profound consequences. Decades on, asphericality conjectures of Arnol?d, Thom, and Kontsevich?Zorich remain largely unsolved, and it has come to be regarded as a significantly challenging topic. This project?s goal is to identify promising-looking inroads. The PI has developed a method called ""Abel-Jacobi flow"" that he proposes to use to establish asphericality of some special strata of Abelian differentials. A successful resolution of this program would constitute a major advance on the Kontsevich?Zorich conjecture; other potential applications are also described. The second main focus is on families of polynomials. This includes linear systems on algebraic surfaces; a program to better understand the fundamental groups is outlined. Two families of univariate polynomials are also discussed, with an eye towards asphericality conjectures: (1) the equicritical stratification and (2) spaces of fewnomials. These are simple enough to be understood concretely, while being complex enough to require new techniques. In addition to topology, the work proposed here promises to inject new examples into geometric group theory. Many of the central objects of interest in the field (braid groups, mapping class groups, Artin groups) are intimately related to algebraic geometry. The fundamental groups of the spaces the PI studies here should be just as rich, and a major goal of the project is to bring this to fruition.

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 47a0fb2..589ca51 100644 --- a/Applied-Mathematics/Awards-Applied-Mathematics-2024.csv +++ b/Applied-Mathematics/Awards-Applied-Mathematics-2024.csv @@ -1,7 +1,9 @@ "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" +"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." +"2408263","Kinetic Transport of Interactive Complex Particle Dynamics in Mean Fields.","DMS","APPLIED MATHEMATICS","09/01/2024","08/22/2024","Irene Gamba","TX","University of Texas at Austin","Standard Grant","Dmitry Golovaty","08/31/2027","$350,000.00","","gamba@math.utexas.edu","110 INNER CAMPUS DR","AUSTIN","TX","787121139","5124716424","MPS","126600","","$0.00","The overall objective of the principal investigator's (PI) research is to develop accurate mathematical models and computer simulations arising from physical phenomena of fundamental scientific interest. The mathematical problems considered in this project describe non-equilibrium systems endowed with memory effects. Such systems are characterized by internal and external forces that generate breaking of symmetry and exhibit stable states that cannot be captured by simple hydrodynamics within classical fluid and gas dynamics modeling. The elements of these systems arise in many phenomena impacting daily human life: e.g., biosystems and molecular medicine at miniature scale, plasma evolution in fusion models for clean energy, and reacting solid state nano structures for solar generation of hydrogen resources, to name just a few. The broad range of problems requires new computational approaches that are being designed and analyzed within this project to ensure consistency, stability, error estimates control and rates of convergence to equilibrium. The scientific computing component is being developed using the techniques that need to be integrated into novel AI and ML strategies along with the tools from non-linear analysis. The work is interdisciplinary in nature and is being carried out in collaboration with physicists, engineers, and social scientists. The PI?s students and postdoc trainees will be involved in the research.

These research goals comprise a broad program in the development of analytical and numerical tools associated with statistical transport equations and systems at the core of applied mathematics in probability, statistics applied to chemistry, physics as well as biological and social dynamics. They concern the modeling of complex interactions systems yielding kinetic frameworks associated to Markovian and non-Markovian processes of birth-death dynamics such as Chapman-Kolmogorov flows of weak turbulence problems arising as dissipative mechanisms in Vlasov-Poisson or Maxwell systems. Such statistical approaches lead to nonlinear integro-differential systems of equations of collisional classical, or quantum Boltzmann of Dirac-Fermi or Bose Einstein type, or aggregation, coalescence, breakage particle systems. The PI will focus on the interplay of this models from analytical and numerical mathematics viewpoint and the scientific computing implementations.

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." "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." -"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." @@ -20,20 +22,20 @@ "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." -"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." +"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." "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." @@ -43,11 +45,10 @@ "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." "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." -"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." +"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." "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/Computational-Mathematics/Awards-Computational-Mathematics-2024.csv b/Computational-Mathematics/Awards-Computational-Mathematics-2024.csv index 72e6d6e..5080952 100644 --- a/Computational-Mathematics/Awards-Computational-Mathematics-2024.csv +++ b/Computational-Mathematics/Awards-Computational-Mathematics-2024.csv @@ -1,6 +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" "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." +"2438562","CAREER: Shape Analysis in Submanifold Spaces: New Directions for Theory and Algorithms","DMS","COMPUTATIONAL MATHEMATICS","08/15/2024","08/21/2024","Nicolas Charon","TX","University of Houston","Continuing Grant","Yuliya Gorb","01/31/2025","$206,254.00","","ncharon@central.uh.edu","4300 MARTIN LUTHER KING BLVD","HOUSTON","TX","772043067","7137435773","MPS","127100","1045, 9263","$0.00","Shape analysis has now become an integral component of data science as it is key to modelling and analyzing quantitatively the geometric variability within datasets for applications as diverse as computer vision, speech/motion recognition, morphogenesis or computational anatomy. Among the variety of geometric structures that are studied in this field, curves, surfaces and more generally manifolds are both very natural objects but also particularly challenging to process and analyze due to the non-canonical structure of the corresponding shape spaces. This has in part hindered the development and effectiveness of shape analysis frameworks for such data, if compared for instance to the more widely studied case of images. This project attempts to bridge a few of these important gaps, both on the theoretical and computational side and develop new scalable algorithms for morphological analysis adapted to the growing size and complexity of real datasets. The project will also promote those research topics among students at various levels of the educational system, with the creation of an upper-level undergraduate course on differential and computational geometry, training of PhD students and K-12 outreach activities through the Women in Science and Engineering (WISE) program in particular.

Building up on several prior works on shape spaces and metrics, the specific research objectives of this project are (1) to advance the analysis and comparison of relaxed shape matching problems deriving from Riemannian metrics on spaces of manifolds; (2) to investigate supervised and unsupervised deep learning approaches to improve the efficiency of manifold registration algorithms; and (3) to study novel extensions of those models to account for partial or incomplete data and model joint shape/topological variations across shapes. As part of this project's outcome, Python pipelines will be developed and made openly accessible to the scientific community with the long term goal of expanding the potential scope of applications of those 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." "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." +"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." "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." @@ -16,7 +18,6 @@ "2410252","Machine Learning-Enabled Self-Consistent Field Theory for Soft Materials","DMS","OFFICE OF MULTIDISCIPLINARY AC, COMPUTATIONAL MATHEMATICS","08/01/2024","07/31/2024","Hector Ceniceros","CA","University of California-Santa Barbara","Standard Grant","Troy D. Butler","07/31/2027","$273,291.00","","hdc@math.ucsb.edu","3227 CHEADLE HALL","SANTA BARBARA","CA","931060001","8058934188","MPS","125300, 127100","075Z, 079Z, 9263","$0.00","Computer simulations are a powerful tool for understanding, predicting, and discovering soft material formulations such as polymer systems. Polymers are composed of long molecular chains and are ubiquitous in both synthetic (e.g., nylon, polyethylene, polyester, Teflon) and natural (e.g., DNA, proteins, cellulose, nucleic acids) settings. In this project, computational tools will be developed that combine machine learning and scientific computing for the exploration and prediction of polymer systems, which will also help to accelerate the discovery of new materials. More broadly, this project will provide a framework for similar computationally costly problems that could be dramatically expedited by using machine learning. Last but not least, the project will serve as an anchor for the interdisciplinary training of both undergraduate and graduate students in an emerging field of much demand.

Parameter space exploration for a soft material is an instance of the forward problem: given a set of parameters, find the corresponding stable morphology. But the inverse design problem, which consists of obtaining the formulation parameters that stabilize a given target morphology, is also of great technological importance as it facilitates the design of new functional materials with highly-tuned and desired properties. The numerical solution of both forward and inverse design problems requires the repeated evaluation of the computationally costly functions. The research team will develop efficient computational methods to enable polymer self-consistent field theory with machine learning to accelerate the solution of both forward and inverse design problems aimed at facilitating the discovery of new structures and the design of polymers and polymer 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." "2409634","Structure-Preserving Linear Schemes for the Diffuse-Interface Models of Incompressible Two-Phase Flows with Matched Densities","DMS","OFFICE OF MULTIDISCIPLINARY AC, COMPUTATIONAL MATHEMATICS","08/01/2024","08/01/2024","Lili Ju","SC","University of South Carolina at Columbia","Standard Grant","Ludmil T. Zikatanov","07/31/2027","$294,473.00","","ju@math.sc.edu","1600 HAMPTON ST","COLUMBIA","SC","292083403","8037777093","MPS","125300, 127100","9150, 9263","$0.00","As a fundamental example of multi-phase flows, two-phase flows are frequently encountered in natural and industrial processes, such as mixing of the fresh water and seawater at the estuaries in marine science, oil and gas transportation in the petroleum industry, the solidification of binary alloys in materials science and so on. The interfaces between the two immiscible fluids play a crucial role in these phenomena, and the diffusive-interface approach have been widely used for their modeling due to its significant advantages in handling topological changes and easiness of implementation. These two-phase flow systems also often possess some crucial physical structures, such as energy stability, bound preservation, and mass conservation. Preservation of these structures is not only a desirable attribute of numerical schemes for their high-fidelity simulations in scientific and engineering applications but also plays a pivotal role in stability and error analysis of the numerical schemes. The project involves diverse research work in computational and applied mathematics, ranging from algorithm design, numerical analysis, to computer implementation. The research results produced from this project will be actively disseminated through publishing papers, giving talks, organizing mini-symposia and workshops, maintaining informative websites, and delivering software codes. Moreover, this project's broader impact also includes its potential to offer an exceptional opportunity for graduate students to engage in diverse interdisciplinary mathematics research.

The primary goal of the project is to develop and analyze efficient, robust, and accurate structure-preserving linear schemes for simulating diffuse-interface models of incompressible two-phase flows with matched densities. In particular, the research activities include 1) the development and analysis of robust energy-stable, decoupled linear schemes for the fluid dynamics equations based on regularization techniques, 2) accurate bound-preserving and energy-stable linear schemes for the phase field equations by utilizing the backward differentiation formulas and the prediction-correction approach, and 3) effective linear relaxation methods with structure preservation for decoupling the fluid dynamics and phase field solvers of the flow system. This project will lead to significant innovations in computational tools with high-efficiency and high-fidelity for simulations of the Navier-Stokes-Allen-Cahn and Navier-Stokes-Cahn-Hilliard systems. In addition, it will offer new insights into outstanding algorithmic issues on bound preservation and energy stability of numerical discretization for two-phase and general multi-phase flows in various scientific and engineering 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." "2408978","Finite element methods for complex surface fluids","DMS","COMPUTATIONAL MATHEMATICS","07/01/2024","05/30/2024","Maxim Olshanskiy","TX","University of Houston","Standard Grant","Yuliya Gorb","06/30/2027","$319,951.00","","molshan@math.uh.edu","4300 MARTIN LUTHER KING BLVD","HOUSTON","TX","772043067","7137435773","MPS","127100","9263","$0.00","Material interfaces with lateral fluidity are widespread in biology and are vital for processes at various scales, from subcellular to tissue levels. Mathematical models describe these interfaces using systems of partial differential equations on deforming surfaces, sometimes linked to equations in the bulk. These equations govern the movement of interfaces and fluid flow along them and in the surrounding medium. While existing studies often focus on simple, homogeneous fluid flows on steady surfaces, real-life scenarios are more complex. This research project will develop and analyze new computational methods for studying these complex fluid systems. In addition, open-source software for simulating evolving surface PDEs will be developed and the project will provide research training opportunities for students.

This project will develop and analyze a finite element method for the tangential fluid system posed on a moving surface, a multi-component surface flow problem, and a fluid-elastic interface model, all arising in the continuum modeling of inextensible viscous deformable membranes. A numerical approach will be employed in the project that falls into the category of geometrically unfitted discretizations. It will allow for large surface deformations, avoid the need for surface parametrization and triangulation, and have optimal complexity. The developed technique will incorporate an Eulerian treatment of time derivatives in evolving domains and employ physics-based stable and linear splitting schemes. The particular problems that will be addressed include the analysis of finite element methods for the Boussinesq-Scriven fluid problem on a passively evolving surface; the development of a stable linear finite element scheme for a phase-field model of two-phase surface flows on both steady and evolving surfaces; and the construction of a splitting scheme for equations governing the motion of a material surface exhibiting lateral fluidity and out-of-plane elasticity.

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." "2410671","Robust Algorithms Based on Domain Decomposition and Microlocal-Analysis for Wave propagation","DMS","COMPUTATIONAL MATHEMATICS","07/01/2024","06/14/2024","Yassine Boubendir","NJ","New Jersey Institute of Technology","Standard Grant","Ludmil T. Zikatanov","06/30/2027","$200,000.00","","boubendi@njit.edu","323 DR MARTIN LUTHER KING JR BLV","NEWARK","NJ","071021824","9735965275","MPS","127100","9263","$0.00","More than ever, technological advances in industries such as aerospace, microchips, telecommunications, and renewable energy rely on advanced numerical solvers for wave propagation. The aim of this project is the development of efficient and accurate algorithms for acoustic and electromagnetic wave propagation in complex domains containing, for example, inlets, cavities, or a multilayer structure. These geometrical features continue to pose challenges for numerical computation. The numerical methods developed in this project will have application to radar, communications, remote sensing, stealth technology, satellites, and many others. Fundamental theoretical and computational issues as well as realistic complex geometries such as those occurring in aircraft and submarines will be addressed in this project. The obtained algorithms will facilitate the use of powerful computers when simulating industrial high-frequency wave problems. The numerical solvers obtained through this research will be made readily available to scientists in aerospace and other industries, which will contribute to enhancing the U.S leadership in this field. Several aspects in this project will benefit the education of both undergraduate and graduate students. Graduate students will gain expertise in both scientific computing and mathematical analysis. This will reinforce their preparation to face future challenges in science and technology.

The aim of this project is the development of efficient and accurate algorithms for acoustic and electromagnetic wave propagation in complex domains. One of the main goals of this project resides in the design of robust algorithms based on high-frequency integral equations, microlocal and numerical analysis, asymptotic methods, and finite element techniques. The investigator plans to derive rigorous asymptotic expansions for incidences more general than plane waves in order to support the high-frequency integral equation multiple scattering iterative procedure. The investigator will introduce Ray-stabilized Galerkin boundary element methods, based on a new theoretical development on ray tracing, to significantly reduce the computational cost at each iteration and limit the exponentially increasing cost of multiple scattering iterations to a fixed number. Using the theoretical findings in conjunction with the stationary phase lemma, frequency-independent quadratures for approximating the multiple scattering amplitude will also be designed. These new methods will be beneficial for industrial applications involving multi-component radar and antenna design. In addition, this project includes development of new non-overlapping domain decomposition methods with considerably enhanced convergence characteristics. The main idea resides in a novel treatment of the continuity conditions in the neighborhood of the so called cross-points. Analysis of the convergence and stability will be included in parallel to numerical simulations in the two and three dimensional cases using high performance computing.

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." "2409903","Development of novel numerical methods for forward and inverse problems in mean field games","DMS","COMPUTATIONAL MATHEMATICS","07/01/2024","06/11/2024","Yat Tin Chow","CA","University of California-Riverside","Continuing Grant","Troy D. Butler","06/30/2027","$95,280.00","","yattinc@ucr.edu","200 UNIVERSTY OFC BUILDING","RIVERSIDE","CA","925210001","9518275535","MPS","127100","9263","$0.00","Mean field games is the study of strategic decision making in large populations where individual players interact through a certain quantity in the mean field. Mean field games have strong descriptive power in socioeconomics and biology, e.g. in the understanding of social cooperation, stock markets, trading and economics, biological systems, election dynamics, population games, robotic control, machine learning, dynamics of multiple populations, pandemic modeling and control as well as vaccination distribution. It is therefore essential to develop accurate numerical methods for large-scale mean field games and their model recovery. However, current computational approaches for the recovery problem are impractical in high dimensions. This project will comprehensively study new computational methods for both large-scale mean field games and their model recovery. The comprehensive plans will cover algorithmic development, theoretical analysis, numerical implementation and practical applications. The project will also involve research on speeding up the forward and inverse problem computations to speed up the computation for mean field game modeling and turn real life mean field game model recovery problems from computationally unaffordable to affordable. The research team will disseminate results through publications, professional presentations, the training of graduate students at the University of California, Riverside as well as through public outreach events that involve public talks and engagement with high school math fairs. The goals of these outreach events are to increase public literacy and public engagement in mathematics, improve STEM education and educator development, and broaden participation of women and underrepresented minorities.

The project will provide novel computational methods for both forward and inverse problems of mean field games. The team will (1) develop two new numerical methods for forward problems in mean field games, namely monotone inclusion with Benamou-Brenier's formulation and extragradient algorithm with moving anchoring; (2) develop three new numerical methods for inverse problems in mean field games with only boundary measurements, namely a three-operator splitting scheme, a semi-smooth Newton acceleration method, and a direct sampling method. Both theoretical analysis and practical implementations will be emphasized. In particular, numerical methods for inverse problems for mean field games, which is a main target of the project, will be designed to work with only boundary measurements. This represents a brand new field in inverse problems and optimization. The project will also seek the simultaneous reconstruction of coefficients in the severely ill-posed case when only noisy boundary measurements from one or two measurement events are available.

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." "2424305","Comparative Study of Finite Element and Neural Network Discretizations for Partial Differential Equations","DMS","COMPUTATIONAL MATHEMATICS","03/15/2024","03/15/2024","Jonathan Siegel","TX","Texas A&M University","Continuing Grant","Yuliya Gorb","07/31/2025","$140,889.00","","jwsiegel@tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","127100","079Z, 9263","$0.00","This research connects two different fields, machine learning from data science and numerical partial differential equations from scientific and engineering computing, through the comparative study of the finite element method and finite neuron method. Finite element methods have undergone decades of study by mathematicians, scientists and engineers in many fields and there is a rich mathematical theory concerning them. They are widely used in scientific computing and modelling to generate accurate simulations of a wide variety of physical processes, most notably the deformation of materials and fluid mechanics. By contrast, deep neural networks are relatively new and have only been widely used in the last decade. In this short time, they have demonstrated remarkable empirical performance on a wide variety of machine learning tasks, most notably in computer vision and natural language processing. Despite this great empirical success, there is still a very limited mathematical understanding of why and how deep neural networks work so well. We hope to leverage the success of deep learning to improve numerical methods for partial differential equations and to leverage the theoretical understanding of the finite element method to better understand deep learning. The interdisciplinary nature of the research will also provide a good training experience for junior researchers. This project will support 1 graduate student each year of the three year project.

Piecewise polynomials represent one of the most important functional classes in approximation theory. In classical approximation theory and numerical methods for partial differential equations, these functional classes are often represented by linear functional spaces associated with a priori given grids, for example, by splines and finite element spaces. In deep learning, function classes are typically represented by a composition of a sequence of linear functions and coordinate-wise non-linearities. One important non-linearity is the rectified linear unit (ReLU) function and its powers (ReLUk). The resulting functional class, ReLUk-DNN, does not form a linear vector space but is rather parameterized non-linearly by a high-dimensional set of parameters. This function class can be used to solve partial differential equations and we call the resulting numerical algorithms the finite neuron method (FNM). Proposed research topics include: error estimates for the finite neuron method, universal construction of conforming finite elements for arbitrarily high order partial differential equations, an investigation into how and why the finite neuron method gives a much better asymptotic error estimate than the corresponding finite element method, and the development and analysis of efficient algorithms for using the finite neuron method.

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 0ce0ba2..a89145d 100644 --- a/Mathematical-Biology/Awards-Mathematical-Biology-2024.csv +++ b/Mathematical-Biology/Awards-Mathematical-Biology-2024.csv @@ -2,14 +2,15 @@ "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." +"2421378","IHBEM: The evolution of human behaviors in the context of emerging diseases and novel vaccines","DMS","MATHEMATICAL BIOLOGY, MSPA-INTERDISCIPLINARY","09/01/2024","08/22/2024","Nicole Creanza","TN","Vanderbilt University","Continuing Grant","Joseph Whitmeyer","08/31/2027","$126,584.00","Glenn Webb","nicole.creanza@vanderbilt.edu","110 21ST AVE S","NASHVILLE","TN","372032416","6153222631","MPS","733400, 745400","068Z, 9178, 9179","$0.00","This project analyzes mathematical models that incorporate the interaction between human behavior and infection transmission of epidemic diseases. The goal is to inform public health policy decisions that are implemented when a major epidemic is spreading throughout a population. The models encompass social acceptance or resistance to public interventions such as social distancing, public closings, individual isolation, mask wearing, and vaccination. The models simulate evolving disease dynamics and address how different policies affect the control of the epidemic progression. The project advances inter-disciplinary perspectives that facilitate more accurate and applicable models of epidemic diseases. Broader Impacts of this project include a mini-unit on public health integrated in K-12 science and math courses and a bridge program. Mentorship is also an emphasis, notably in a bridge program between Masters and PhD levels to increase diversity in science.


Three classes of models are developed: (1) Agent based models that track individual behavior connected to vaccine hesitancy and public vaccination information; (2) Multi-layered discrete time network models that access the impact of pandemic related cultural shifts and risk perception of disease spread and vaccination acceptance; (3) Compartment differential equations models that incorporate dynamic changes in individual chronological age related human behavior and individual vaccination stages. Data are obtained from the Centers of Disease Control and Prevention, the New York State Department of Health, the National Center for Immunization, and other epidemic data sources.

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." +"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." +"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." "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."