From 72d430584876384ba573d3a7423f3dfe204cee2c Mon Sep 17 00:00:00 2001 From: Yimin Zhong Date: Sun, 25 Aug 2024 06:37:11 +0000 Subject: [PATCH] Update Awards --- .../Awards-Algebra-and-Number-Theory-2024.csv | 11 ++++++----- Combinatorics/Awards-Combinatorics-2024.csv | 3 ++- .../Awards-Mathematical-Biology-2024.csv | 6 ++++-- Statistics/Awards-Statistics-2024.csv | 3 ++- Topology/Awards-Topology-2024.csv | 19 ++++++++++--------- 5 files changed, 24 insertions(+), 18 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 920cb96..d7cc06c 100644 --- a/Algebra-and-Number-Theory/Awards-Algebra-and-Number-Theory-2024.csv +++ b/Algebra-and-Number-Theory/Awards-Algebra-and-Number-Theory-2024.csv @@ -1,4 +1,5 @@ "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" +"2423898","Conference: Number Theory Meetings in the Southeast","DMS","ALGEBRA,NUMBER THEORY,AND COM","09/01/2024","08/23/2024","Frank Thorne","SC","University of South Carolina at Columbia","Standard Grant","Andrew Pollington","08/31/2025","$22,508.00","Matthew Boylan, Hui Xue, Robert Dicks, Wei-Lun Tsai","thorne@math.sc.edu","1600 HAMPTON ST","COLUMBIA","SC","292083403","8037777093","MPS","126400","7556, 9150","$0.00","This grant, together with a grant from the National Security Agency, will fund a series of three regional number theory conferences in the Southeast: the Palmetto Number Theory Series at Wake Forest University, Winston-Salem, NC on September 21-22, 2024 and again at the University of South Carolina, Columbia, SC in December 2024, and the Southeast Regional Meeting on Numbers in Savannah, GA in Spring 2025. The meetings consist of participant talks on current research in all areas of number theory, including analytic number theory, arithmetic geometry, and automorphic and modular forms. These topics reflect the research interests of number theorists working in the Southeast. Each meeting features plenary talks by nationally and internationally recognized leaders in the field, invited talks by graduate students and postdoctoral researchers, and a larger number of contributed talks by mathematicians at all levels including undergraduate and graduate students, and junior and senior faculty. Number theorists from outside the Southeast will give the invited and plenary talks, while regional researchers will give most of the contributed talks. Attendance is free of charge, and all are welcome.

A primary goal of the Southeastern Number Theory Meetings is to provide members of the number theory community in the Southeast with an opportunity to learn about new and significant research in number theory and to disseminate their own research. Students and junior researchers in the community particularly benefit from the meetings. The meetings strengthen their knowledge base, expose their work to a wider audience, and give them insightful input and feedback from other participants. Funding from the NSF allows the organizers to achieve their goals at a low cost to individual participants. These meetings integrate regional mathematicians into the community who may have little or no funds for professional travel such as graduate students and faculty at institutions that do not award Ph.Ds. The organizers will continue efforts to attract a demographically diverse participant base including women and racial and ethnic minorities. Further information on these meetings will including the locations, dates, lists of speakers, lists of participants, and registration information will be linked to the conference home pages as it becomes available: https://people.math.sc.edu/boylan/seminars/pantshome.html and https://huixue.people.clemson.edu/SERMON.html.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "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." @@ -34,10 +35,10 @@ "2401662","Conference: Southern Regional Algebra Conference 2024","DMS","ALGEBRA,NUMBER THEORY,AND COM","03/15/2024","01/18/2024","Jean Nganou","TX","University of Houston - Downtown","Standard Grant","Tim Hodges","02/28/2025","$14,990.00","","nganouj@uhd.edu","1 MAIN ST","HOUSTON","TX","770021014","7132218005","MPS","126400","7556","$0.00","This award supports participation in the Southern Regional Algebra Conference (SRAC). The SRAC is a yearly weekend conference that has been in existence since 1988. Its first edition was held at the University of Southern Mississippi in the Spring of 1988. This spring the SRAC will be held at the University of Houston-Downtown, March 22-24, 2024. The SRAC brings together mathematicians that carry out research in the area of algebra and closely related areas for a full weekend of lectures, short presentations and discussions. The conference attracts researchers from many undergraduate institutions in the Gulf Coast Region that usually do not have sufficient funding to support their research activities, especially long-distance meetings. It is also an important platform for graduate students and early career mathematicians to present their research in algebra and be exposed to a community of algebraists outside their respective home institutions.

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -95,8 +96,8 @@ "2347097","Collaborative Research: Conference: Texas-Oklahoma Representations and Automorphic forms (TORA)","DMS","ALGEBRA,NUMBER THEORY,AND COM","01/01/2024","12/19/2023","Melissa Emory","OK","Oklahoma State University","Standard Grant","Andrew Pollington","12/31/2026","$20,000.00","Maria Fox, Mahdi Asgari","melissa.emory@okstate.edu","401 WHITEHURST HALL","STILLWATER","OK","740781031","4057449995","MPS","126400","7556, 9150","$0.00","This award supports the TORA mathematics conference series. This series consists of annual meetings hosted by the University of North Texas, Oklahoma State University, and the University of Oklahoma on a rotating basis. This award provides support for three weekend conferences, one at the University of North Texas in Spring 2024 (TORA XIII), one at Oklahoma State University in Spring 2025 (TORA XIV), and another at the University of Oklahoma in Spring 2026 (TORA XV). Each conference will feature three prominent guest speakers from outside the Texas-Oklahoma region, in addition to other participants including students, post-doctoral researchers, and junior faculty. Regional graduate students and researchers will also give talks describing their work. These conferences will facilitate collaborations and interactions among the students and researchers in the region who work in the areas of Automorphic Forms, Representation Theory, and Number Theory.

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



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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -109,10 +110,10 @@ "2401422","Algebraic Geometry and Strings","DMS","ALGEBRA,NUMBER THEORY,AND COM","07/01/2024","04/09/2024","Ron Donagi","PA","University of Pennsylvania","Continuing Grant","Adriana Salerno","06/30/2028","$95,400.00","","donagi@math.upenn.edu","3451 WALNUT ST STE 440A","PHILADELPHIA","PA","191046205","2158987293","MPS","126400","","$0.00","Exploration of the interactions of physical theories (string theory and quantum field theory) with mathematics (especially algebraic geometry) has been extremely productive for decades, and the power of this combination of tools and approaches only seems to strengthen with time. The goal of this project is to explore and push forward some of the major issues at the interface of algebraic geometry with string theory and quantum field theory. The research will employ and combine a variety of techniques from algebraic geometry, topology, integrable systems, String theory, and Quantum Field theory. The project also includes many broader impact activities such as steering and organization of conferences and schools, membership of international boards and prize committees, revising Penn?s graduate program, curricular development at the graduate and undergraduate level, advising postdocs, graduate and undergraduate students, editing several public service volumes and editing of journals and proceedings volumes.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -120,10 +121,10 @@ "2334874","Conference: Pittsburgh Links among Analysis and Number Theory (PLANT)","DMS","ALGEBRA,NUMBER THEORY,AND COM, ANALYSIS PROGRAM","02/01/2024","01/19/2024","Carl Wang Erickson","PA","University of Pittsburgh","Standard Grant","James Matthew Douglass","01/31/2025","$20,000.00","Theresa Anderson, Armin Schikorra","carl.wang-erickson@pitt.edu","4200 FIFTH AVENUE","PITTSBURGH","PA","152600001","4126247400","MPS","126400, 128100","7556","$0.00","This award will support the four-day conference ""Pittsburgh Links among Analysis and Number Theory (PLANT)"" that will take place March 4-7, 2024 in Pittsburgh, PA. The purpose of the conference is to bring together representatives of two disciplines with a shared interface: number theory and analysis. There is a large potential for deeper collaboration between these fields resulting in new and transformative mathematical perspectives, and this conference aims at fostering such an interchange. In particular, the conference is designed to attract PhD students and post-doctoral scholars into working on innovations at this interface.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." diff --git a/Combinatorics/Awards-Combinatorics-2024.csv b/Combinatorics/Awards-Combinatorics-2024.csv index 022f2f9..fc23b61 100644 --- a/Combinatorics/Awards-Combinatorics-2024.csv +++ b/Combinatorics/Awards-Combinatorics-2024.csv @@ -1,5 +1,6 @@ "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract" -"2435236","Conference: The KOI Combinatorics Lectures","DMS","Combinatorics","09/01/2024","08/19/2024","Mihai Ciucu","IN","Indiana University","Continuing Grant","Stefaan De Winter","08/31/2027","$15,260.00","Margaret Readdy, Richard Ehrenborg, Eric Katz, Saul Blanco Rodriguez","mciucu@indiana.edu","107 S INDIANA AVE","BLOOMINGTON","IN","474057000","3172783473","MPS","797000","7556","$0.00","The 3rd KOI Combinatorics Lectures will be held October 4-5, 2024 at Indiana University. This regional conference is organized by members of the combinatorics community from the Kentucky, Ohio and Indiana (KOI) area. It seeks to rebuild and initiate research connections among the KOI area graduate students, postdocs and faculty, including individuals from over thirty nearby small colleges, regional universities and ethnically diverse colleges. The conference program consists of four talks from emerging and established researchers in combinatorics broadly defined, a problem session, and a poster session that is open to all participants. In Japanese culture, koi symbolize strength, courage, patience and success through perseverance. All of the conference activities serve to strengthen these attributes among the participants, with a strong focus on increasing the numbers of underrepresented groups in the mathematical sciences, including women. The follow-up yearly conferences will continue at the University of Kentucky in 2025 and the Ohio State University in 2026.


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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2348701","Positivity in Tropical Geometry and Combinatorics","DMS","Combinatorics","09/01/2024","08/23/2024","Josephine Yu","GA","Georgia Tech Research Corporation","Continuing Grant","Stefaan De Winter","08/31/2027","$60,319.00","","jyu@math.gatech.edu","926 DALNEY ST NW","ATLANTA","GA","303186395","4048944819","MPS","797000","","$0.00","Classical algebraic geometry studies solution spaces of systems of algebraic equations, which arise naturally in many areas of sciences and engineering. Although the solutions over complex numbers are better understood, the solutions over real numbers or positive numbers are often more meaningful in the contexts where the equations arise. The PI will use the modern technique of tropical geometry to study real and positive solutions of systems of polynomial equations in many unknowns. Tropical mathematics arises over the (max,plus)-algebra where addition is replaced by taking the maximum and multiplication is replaced by the usual addition. The tropical equations are often easier to solve, and some discrete features of the solution set over real or complex numbers can be computed from the solution set over the tropical numbers. This project aims at developing the tropical geometry specifically for solving equations over real numbers or positive numbers. Applications include development of new computational tools with applications in optimization. The PI will continue her work on mentoring postdocs, graduate students, and undergraduate students; organization of conferences; outreach to K-12 students; and promotion of inclusiveness and equity in the mathematical sciences.

The PI will study important classes of real algebraic varieties and real semialgebraic sets using tropical geometry. These families include determinantal varieties, nonnegative and sums-of-squares polynomials, principal minors of positive semidefinite matrices, stable and Lorentzian polynomials, discriminants and resultants, and semialgebraic sets arising from positivity in polytope theory including Ehrhart theory and the theory of Minkowski weights. In particular, the PI will investigate computational problems, topology properties, and lifting problems for inequalities from tropical to classical algebraic geometry. The proposed work will promote interactions among various fields of mathematics and advance knowledge in foundations of tropical geometry, real algebraic geometry, and geometric combinatorics. The proposed problems have connections to optimization (low rank matrix completion, nonnegative and sum-of-square polynomials), computational algebra (principal minor assignment problem, discriminants and resultants), and convex geometry and polytope theory (Christoffel?Minkowski problem, weighted Ehrhart theory).

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


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

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

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

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

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

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." diff --git a/Mathematical-Biology/Awards-Mathematical-Biology-2024.csv b/Mathematical-Biology/Awards-Mathematical-Biology-2024.csv index a89145d..e40ba4a 100644 --- a/Mathematical-Biology/Awards-Mathematical-Biology-2024.csv +++ b/Mathematical-Biology/Awards-Mathematical-Biology-2024.csv @@ -1,13 +1,15 @@ "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract" +"2424827","Collaborative Research: eMB: Data-driven mechano-chemical models of morphogenesis on deforming domains","DMS","MATHEMATICAL BIOLOGY","09/01/2024","08/23/2024","Jeremiah Zartman","IN","University of Notre Dame","Standard Grant","Amina Eladdadi","08/31/2027","$257,591.00","Zhiliang Xu, Alexander Dowling","jzartman@nd.edu","940 GRACE HALL","NOTRE DAME","IN","465565708","5746317432","MPS","733400","079Z, 8038","$0.00","This is a collaborative project between the University of California-Riverside and University of Notre Dame. A critical challenge in biology is to understand the emergent multicellular features of organ development involving both intracellular processes and cell-cell interactions. This project will focus on investigating a critical late-stage phase of fruit fly wing disc development, called eversion, which undergoes a significant shape change and serves as a model of epithelial remodeling. These same mechanisms are also involved in the development, wound healing and cancer progression. Subsequent morphogenetic processes fully define the adult wing, hinge, and notum to generate the final adult organ structures. Individual cell shape changes lead to extensive tissue deformations during eversion. The proposed study combining modeling and experimentation will provide mechanistic insights into how hormonal signaling, morphogen-driven pattern formation, and cytoskeletal regulators synergistically impact epithelial organ architecture. The newly developed multiscale mathematical and computational modeling and machine learning approaches enable predictive design-based approaches for regenerative medicine and stem cell engineering. University of California-Riverside (UCR) is a Hispanic-serving institution located in one of the most ethnically diverse areas of the country. Many students are the first in their families to attend college. To increase the diversity of students pursuing graduate education in mathematical biology, applied mathematics and bioengineering, the PIs will partner with UCR?s Mentoring Summer Research Internship Program and UCR?s GradEdge/Jumpstart Programs for undergraduate and graduate students from underrepresented groups. Additionally, the PIs at Notre Dame will offer summer research internships to undergraduate students with focused recruitment from underrepresented groups and facilitate cross-disciplinary mentorship of trainees on both campuses.

A central, unsolved problem in biology is elucidating the collective molecular mechanisms regulating cell shapes and how these determine the emergent systems-level generating organ shape formation (morphogenesis). The robust morphogenesis of multilayered tissues requires the coordination of a repertoire of cellular processes akin to ?unit operations,? including: cellular mass regulation (cell growth, proliferation, and death), cell-environment regulation (cell-cell and cell-substrate adhesion), and cell mechanical regulation (the membrane and cytoskeletal elasticity, cytoskeleton-centered tension, cytosolic pressure). Combining these cellular processes creates the final tissue-scale architecture through a sophisticated communication network. Many congenital disabilities and degenerative diseases result from dysregulation of these unit operations. Thus, it is critical to decipher the complex mechanisms that integrate biochemical and mechanical signals to define emergent organ shape. This project utilizes the fruit fly wing imaginal disc to elucidate the critical signaling pathways and conserved biophysical mechanisms that are functionally significant for organ development and epithelial cell function. This project will develop new multiscale mathematical and computational modeling approaches on 3D deforming domains to simulate multicellular wing disc morphogenesis. Key innovations will include simulation acceleration via neural networks. The new models will be calibrated using experimental data incorporating genetic perturbations and immunohistochemistry and machine learning methods to elucidate the mechanisms integrating mechanical and biochemical regulatory networks during organogenesis. Data-driven and machine learning-enabled pipeline will systematize the calibration of candidate models and enable optimization of the experimental design for validating model predictions and testing mechanisms of morphogenesis.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "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." +"2424826","Collaborative Research: eMB: Data-driven mechano-chemical models of morphogenesis on deforming domains","DMS","MATHEMATICAL BIOLOGY","09/01/2024","08/23/2024","Mark Alber","CA","University of California-Riverside","Standard Grant","Amina Eladdadi","08/31/2027","$227,747.00","Weitao Chen","malber@ucr.edu","200 UNIVERSTY OFC BUILDING","RIVERSIDE","CA","925210001","9518275535","MPS","733400","079Z, 8038","$0.00","This is a collaborative project between the University of California-Riverside and University of Notre Dame. A critical challenge in biology is to understand the emergent multicellular features of organ development involving both intracellular processes and cell-cell interactions. This project will focus on investigating a critical late-stage phase of fruit fly wing disc development, called eversion, which undergoes a significant shape change and serves as a model of epithelial remodeling. These same mechanisms are also involved in the development, wound healing and cancer progression. Subsequent morphogenetic processes fully define the adult wing, hinge, and notum to generate the final adult organ structures. Individual cell shape changes lead to extensive tissue deformations during eversion. The proposed study combining modeling and experimentation will provide mechanistic insights into how hormonal signaling, morphogen-driven pattern formation, and cytoskeletal regulators synergistically impact epithelial organ architecture. The newly developed multiscale mathematical and computational modeling and machine learning approaches enable predictive design-based approaches for regenerative medicine and stem cell engineering. University of California-Riverside (UCR) is a Hispanic-serving institution located in one of the most ethnically diverse areas of the country. Many students are the first in their families to attend college. To increase the diversity of students pursuing graduate education in mathematical biology, applied mathematics and bioengineering, the PIs will partner with UCR?s Mentoring Summer Research Internship Program and UCR?s GradEdge/Jumpstart Programs for undergraduate and graduate students from underrepresented groups. Additionally, the PIs at Notre Dame will offer summer research internships to undergraduate students with focused recruitment from underrepresented groups and facilitate cross-disciplinary mentorship of trainees on both campuses.

A central, unsolved problem in biology is elucidating the collective molecular mechanisms regulating cell shapes and how these determine the emergent systems-level generating organ shape formation (morphogenesis). The robust morphogenesis of multilayered tissues requires the coordination of a repertoire of cellular processes akin to ?unit operations,? including: cellular mass regulation (cell growth, proliferation, and death), cell-environment regulation (cell-cell and cell-substrate adhesion), and cell mechanical regulation (the membrane and cytoskeletal elasticity, cytoskeleton-centered tension, cytosolic pressure). Combining these cellular processes creates the final tissue-scale architecture through a sophisticated communication network. Many congenital disabilities and degenerative diseases result from dysregulation of these unit operations. Thus, it is critical to decipher the complex mechanisms that integrate biochemical and mechanical signals to define emergent organ shape. This project utilizes the fruit fly wing imaginal disc to elucidate the critical signaling pathways and conserved biophysical mechanisms that are functionally significant for organ development and epithelial cell function. This project will develop new multiscale mathematical and computational modeling approaches on 3D deforming domains to simulate multicellular wing disc morphogenesis. Key innovations will include simulation acceleration via neural networks. The new models will be calibrated using experimental data incorporating genetic perturbations and immunohistochemistry and machine learning methods to elucidate the mechanisms integrating mechanical and biochemical regulatory networks during organogenesis. Data-driven and machine learning-enabled pipeline will systematize the calibration of candidate models and enable optimization of the experimental design for validating model predictions and testing mechanisms of morphogenesis.

This award reflects 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." "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." "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." -"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." +"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." "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." diff --git a/Statistics/Awards-Statistics-2024.csv b/Statistics/Awards-Statistics-2024.csv index 31f3d13..3cb88d1 100644 --- a/Statistics/Awards-Statistics-2024.csv +++ b/Statistics/Awards-Statistics-2024.csv @@ -1,4 +1,6 @@ "AwardNumber","Title","NSFOrganization","Program(s)","StartDate","LastAmendmentDate","PrincipalInvestigator","State","Organization","AwardInstrument","ProgramManager","EndDate","AwardedAmountToDate","Co-PIName(s)","PIEmailAddress","OrganizationStreet","OrganizationCity","OrganizationState","OrganizationZip","OrganizationPhone","NSFDirectorate","ProgramElementCode(s)","ProgramReferenceCode(s)","ARRAAmount","Abstract" +"2412832","Collaborative Research: Statistical Modeling and Inference for Object-valued Time Series","DMS","STATISTICS","07/01/2024","06/17/2024","Changbo Zhu","IN","University of Notre Dame","Continuing Grant","Jun Zhu","06/30/2027","$56,755.00","","czhu4@nd.edu","940 GRACE HALL","NOTRE DAME","IN","465565708","5746317432","MPS","126900","","$0.00","Random objects in general metric spaces have become increasingly common in many fields. For example, the intraday return path of a financial asset, the age-at-death distributions, the annual composition of energy sources, social networks, phylogenetic trees, and EEG scans or MRI fiber tracts of patients can all be viewed as random objects in certain metric spaces. For many endeavors in this area, the data being analyzed is collected with a natural ordering, i.e., the data can be viewed as an object-valued time series. Despite its prevalence in many applied problems, statistical analysis for such time series is still in its early development. A fundamental difficulty of developing statistical techniques is that the spaces where these objects live are nonlinear and commonly used algebraic operations are not applicable. This research project aims to develop new models, methodology and theory for the analysis of object-valued time series. Research results from the project will be disseminated to the relevant scientific communities via publications, conference and seminar presentations. The investigators will jointly mentor a Ph.D. student and involve undergraduate students in the research, as well as offering advanced topic courses to introduce the state-of-the-art techniques in object-valued time series analysis.

The project will develop a systematic body of methods and theory on modeling and inference for object-valued time series. Specifically, the investigators propose to (1) develop a new autoregressive model for distributional time series in Wasserstein geometry and a suite of tools for model estimation, selection and diagnostic checking; (2) develop new specification testing procedures for distributional time series in the one-dimensional Euclidean space; and (3) develop new change-point detection methods to detect distribution shifts in a sequence of object-valued time series. The above three projects tackle several important modeling and inference issues in the analysis of object-valued time series, the investigation of which will lead to innovative methodological and theoretical developments, and lay groundwork for this emerging field.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2413491","ABCel: An Empirical Likelihood-based Method for Approximate Bayesian Computation","DMS","OFFICE OF MULTIDISCIPLINARY AC, STATISTICS","09/01/2024","08/23/2024","Sanjay Chaudhuri","NE","University of Nebraska-Lincoln","Standard Grant","Tapabrata Maiti","08/31/2027","$160,000.00","","schaudhuri2@unl.edu","2200 VINE ST # 830861","LINCOLN","NE","685032427","4024723171","MPS","125300, 126900","9150","$0.00","This project will develop a new, efficient, easy-to-use, and well-justified methodology called ABCel for a purely data-driven statistical inference for many complex models routinely used in natural, engineering, social, and environmental sciences. Examples of such models include phylogenetic trees, dynamical systems, exponential random graph models, etc. Due to the complexity and size of the underlying model classes traditional parameter-based statistical procedures cannot be employed here. The ABCel procedure would draw inferences by comparing the observed data set and multiple new data sets simulated from the model for various values of its parameters. It will require almost no tuning?it could be used off the rack, making it easier to benefit collaborative projects on the spread of diseases (e.g., AIDS, STDs, certain kinds of addictions), monitoring terrorists and similar networks, modeling networks in social media, DEI research, poverty mapping, precision agriculture, and many other fields of study. The project will mentor graduate students, develop course modules, short courses, and several user-friendly software based on the obtained results.

The ABCel procedure is a new empirical likelihood-based methodology for Approximate Bayesian Computation (ABC) used for analyzing processes with intractable likelihoods. Such processes allow easy simulation of multiple data sets for any input value of their parameters. However, they behave like a ""black box"", i.e. because of the complexity and size of the underlying model classes, it is impossible to compute the likelihood of any parameter value. Traditional ABC methods are typically computationally intensive, and not very well-justified. Furthermore, they often require specification of tolerances, smoothing parameters, and distances which crucially affect their performances. For the ABCel procedure, the only inputs required will be a choice of summary statistics, their observed values, and the ability to simulate the chosen summaries for any parameter input. Unlike the traditional ABC methods, no tuning parameters as described above will be required. The parameter posterior will be approximated using an empirical likelihood computed using estimating equations only based on the observed and newly generated summary values. The project will find rigorous justification for the approximation using information theory. Appropriate statistical performance guarantees for the method will be furnished. The team will explore the consistency of the approximate posterior, and its performance under a growing number of samples, replication, and summaries. The procedure will be applied to a detailed analysis of exponential random graph models (ERGM). Such models of social networks are routinely used in epidemiology, sociometry, criminology, national defense, agronomy, small-area estimation, etc.

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

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

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

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

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

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -57,7 +59,6 @@ "2413747","Collaborative Research: NSF MPS/DMS-EPSRC: Stochastic Shape Processes and Inference","DMS","STATISTICS","08/01/2024","06/20/2024","Sebastian Kurtek","OH","Ohio State University","Standard Grant","Yulia Gel","07/31/2027","$199,555.00","","kurtek.1@osu.edu","1960 KENNY RD","COLUMBUS","OH","432101016","6146888735","MPS","126900","1269, 7929","$0.00","The intimate link between form, or shape, and function is ubiquitous in science. In biology, for instance, the shapes of biological components are pivotal in understanding patterns of normal behavior and growth; a notable example is protein shape, which contributes to our understanding of protein function and classification. This project, led by a team of investigators from the USA and the UK, will develop ways of modeling how biological and other shapes change with time, using formal statistical frameworks that capture not only the changes themselves, but how these changes vary across objects and populations. This will enable the study of the link between form and function in all its variability. As example applications, the project will develop models for changes in cell morphology and topology during motility and division, and changes in human posture during various activities, facilitating the exploration of scientific questions such as how and why cell division fails, or how to improve human postures in factory tasks. These are proofs of concept, but the methods themselves will have much wider applicability. This project will thus not only progress the science of shape analysis and the specific applications studied; it will have broader downstream impacts on a range of scientific application domains, providing practitioners with general and useful tools.

While there are several approaches for representing and analyzing static shapes, encompassing curves, surfaces, and complex structures like trees and shape graphs, the statistical modeling and analysis of dynamic shapes has received limited attention. Mathematically, shapes are elements of quotient spaces of nonlinear manifolds, and shape changes can be modeled as stochastic processes, termed shape processes, on these complex spaces. The primary challenges lie in adapting classical modeling concepts to the nonlinear geometry of shape spaces and in developing efficient statistical tools for computation and inference in such very high-dimensional, nonlinear settings. The project consists of three thrust areas, dealing with combinations of discrete and continuous time, and discrete and continuous representations of shape, with a particular emphasis on the issues raised by topology changes. The key idea is to integrate spatiotemporal registration of objects and their evolution into the statistical formulation, rather than treating them as pre-processing steps. This project will specifically add to the current state-of-the-art in topic areas such as stochastic differential equations on shape manifolds, time series models for shapes, shape-based functional data analysis, and modeling and inference on infinite-dimensional shape spaces.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2413833","Collaborative Research: Nonparametric Learning in High-Dimensional Survival Analysis for causal inference and sequential decision making","DMS","STATISTICS","07/01/2024","06/18/2024","Shanshan Ding","DE","University of Delaware","Standard Grant","Jun Zhu","06/30/2027","$200,000.00","Wei Qian","sding@udel.edu","220 HULLIHEN HALL","NEWARK","DE","197160099","3028312136","MPS","126900","9150","$0.00","Data with survival outcomes are commonly encountered in real-world applications to capture the time duration until a specific event of interest occurs. Nonparametric learning for high dimensional survival data offers promising avenues in practice because of its ability to capture complex relationships and provide comprehensive insights for diverse problems in medical and business services, where vast covariates and individual metrics are prevalent. This project will significantly advance the methods and theory for nonparametric learning in high-dimensional survival data analysis, with a specific focus on causal inference and sequential decision making problems. The study will be of interest to practitioners in various fields, particularly providing useful methods for medical researchers to discover relevant risk factors, assess causal treatment effects, and utilize personalized treatment strategies in contemporary health sciences. It will also provide useful analytics tools beneficial to financial and related institutions for assessing user credit risks and facilitating informed decisions through personalized services. The theoretical and empirical studies to incorporate complex nonparametric structures in high-dimensional survival analysis, together with their interdisciplinary applications, will create valuable training and research opportunities for graduate and undergraduate students, including those from underrepresented minority groups.

Under flexible nonparametric learning frameworks, new embedding methods and learning algorithms will be developed for high dimensional survival analysis. First, the investigators will develop supervised doubly robust linear embedding and supervised nonlinear manifold learning method for supervised dimension reduction of high dimensional survival data, without imposing stringent model or distributional assumptions. Second, a robust nonparametric learning framework will be established for estimating causal treatment effect for high dimensional survival data that allows the covariate dimension to grow much faster than the sample size. Third, motivated by applications in personalized service, the investigators will develop a new nonparametric multi-stage algorithm for high dimensional censored bandit problems that allows flexibility with potential non-linear decision boundaries with optimal regret guarantees.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2412895","Statistical Entropic Optimal Transport: Theory, Methods and Applications","DMS","STATISTICS","07/01/2024","06/17/2024","Gonzalo Mena","PA","Carnegie-Mellon University","Continuing Grant","Yong Zeng","06/30/2027","$62,726.00","","gmena@andrew.cmu.edu","5000 FORBES AVE","PITTSBURGH","PA","152133815","4122688746","MPS","126900","075Z, 079Z","$0.00","Optimal transport provides a sensible mathematical framework to address the fundamental statistical question of how a statistician measures the distance between two distributions based on possibly large high-dimensional datasets. A variation of the original transportation problem featuring an entropic penalization has appeared as a more scalable alternative, fueling a wave of new results and successful applications in domains such as genomics, neuroscience, and economics, to name a few. Despite its practical success and the achieved understanding of some of its fundamental statistical properties, there is still a substantial gap between theory and practice in the entropic optimal transport framework. This project will bridge this gap through new methods grounded in an improved theoretical understanding of entropic optimal transport, potentially generating an innovative set of applications in the life sciences. Graduate students will be trained within the scope of this project.


The core of this project focuses on two intimately related thrusts: first, to develop a foundation for inference in parametric models with entropic optimal transport and to identify the regimes for which this framework is best suited. This includes the problem of model-based clustering in high-dimensional, non-asymptotic regimes and a study of the robustness of entropic-optimal-transport estimators. Second, the PIs will develop statistical applications of entropic optimal transport in Alzheimer?s disease neuropathology and spatial transcriptomics.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2412832","Collaborative Research: Statistical Modeling and Inference for Object-valued Time Series","DMS","STATISTICS","07/01/2024","06/17/2024","Changbo Zhu","IN","University of Notre Dame","Continuing Grant","Jun Zhu","06/30/2027","$56,755.00","","czhu4@nd.edu","836 GRACE HALL","NOTRE DAME","IN","465566031","5746317432","MPS","126900","","$0.00","Random objects in general metric spaces have become increasingly common in many fields. For example, the intraday return path of a financial asset, the age-at-death distributions, the annual composition of energy sources, social networks, phylogenetic trees, and EEG scans or MRI fiber tracts of patients can all be viewed as random objects in certain metric spaces. For many endeavors in this area, the data being analyzed is collected with a natural ordering, i.e., the data can be viewed as an object-valued time series. Despite its prevalence in many applied problems, statistical analysis for such time series is still in its early development. A fundamental difficulty of developing statistical techniques is that the spaces where these objects live are nonlinear and commonly used algebraic operations are not applicable. This research project aims to develop new models, methodology and theory for the analysis of object-valued time series. Research results from the project will be disseminated to the relevant scientific communities via publications, conference and seminar presentations. The investigators will jointly mentor a Ph.D. student and involve undergraduate students in the research, as well as offering advanced topic courses to introduce the state-of-the-art techniques in object-valued time series analysis.

The project will develop a systematic body of methods and theory on modeling and inference for object-valued time series. Specifically, the investigators propose to (1) develop a new autoregressive model for distributional time series in Wasserstein geometry and a suite of tools for model estimation, selection and diagnostic checking; (2) develop new specification testing procedures for distributional time series in the one-dimensional Euclidean space; and (3) develop new change-point detection methods to detect distribution shifts in a sequence of object-valued time series. The above three projects tackle several important modeling and inference issues in the analysis of object-valued time series, the investigation of which will lead to innovative methodological and theoretical developments, and lay groundwork for this emerging field.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2412403","Robust Extensions to Bayesian Regression Trees for Complex Data","DMS","STATISTICS","08/01/2024","06/17/2024","HENGRUI LUO","TX","William Marsh Rice University","Continuing Grant","Tapabrata Maiti","07/31/2027","$58,710.00","","hl180@rice.edu","6100 MAIN ST","Houston","TX","770051827","7133484820","MPS","126900","","$0.00","This project is designed to extend the capabilities of tree-based models within the context of machine learning. Tree-based models allow for decision-making based on clear, interpretable rules and are widely adopted in diagnostic and learning tasks. This project will develop novel methodologies to enhance their robustness. Specifically, the research will integrate deep learning techniques with tree-based statistical methods to create models capable of processing complex, high-dimensional data from medical imaging, healthcare, and AI sectors. These advancements aim to significantly improve prediction and decision-making processes, enhancing efficiency and accuracy across a broad range of applications. The project also prioritizes inclusivity and education by integrating training components, thereby advancing scientific knowledge and disseminating results through publications and presentations.

The proposed research leverages Bayesian hierarchies and transformation techniques on trees to develop models capable of managing complex transformations of input data. These models will be tailored to improve interpretability, scalability, and robustness, overcoming current limitations in non-parametric machine learning applications. The project will utilize hierarchical layered structures, where outputs from one tree serve as inputs to subsequent trees, forming network architectures that enhance precision in modeling complex data patterns and relationships. Bayesian techniques will be employed to effectively quantify uncertainty and create ensembles, providing reliable predictions essential for critical offline prediction and real-time decision-making processes. This initiative aims to develop pipelines and set benchmarks for the application of tree-based models across diverse scientific and engineering 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." "2412015","Statistical methods for point-process time series","DMS","STATISTICS","07/01/2024","06/17/2024","Daniel Gervini","WI","University of Wisconsin-Milwaukee","Standard Grant","Jun Zhu","06/30/2027","$149,989.00","","gervini@uwm.edu","3203 N DOWNER AVE # 273","MILWAUKEE","WI","532113188","4142294853","MPS","126900","","$0.00","This research project will develop statistical models and inference methods for the analysis of random point processes. Random point processes are events that occur at random in time or space according to certain patterns; this project will provide methods for the discovery and analysis of such patterns. Examples of events that can be modelled as random point processes include cyberattacks on a computer network, earthquakes, crimes in a city, spikes of neural activity in humans and animals, car crashes in a highway, and many others. Therefore, the methods to be developed under this project will find applications in many fields, such as national security, economy, neuroscience and geosciences, among others. The project will also provide training opportunities for graduate and undergraduate students in the field of Data Science.

This project will specifically develop statistical tools for the analysis of time series of point processes, that is, for point processes that are observed repeatedly over time; for example, when the spatial distribution of crime in a city is observed for several days. These tools will include trend estimation methods, autocorrelation estimation methods, and autoregressive models. Research activities in this project include the development of parameter estimation procedures, their implementation in computer programs, the study of theoretical large sample properties of these methods, the study of small sample properties by simulation, and their application to real-data problems. Other activities in this project include educational activities, such as the supervision of Ph.D. and Master's students, and the development of graduate and undergraduate courses in Statistics and Data Science.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2412408","Monitoring time series in structured function spaces","DMS","STATISTICS","07/01/2024","06/14/2024","Piotr Kokoszka","CO","Colorado State University","Standard Grant","Yulia Gel","06/30/2027","$292,362.00","","Piotr.Kokoszka@colostate.edu","601 S HOWES ST","FORT COLLINS","CO","805212807","9704916355","MPS","126900","1269","$0.00","This project aims to develop new mathematical theory and statistical tools that will enable monitoring for changes in complex systems, for example global trade networks. Comprehensive databases containing details of trade between almost all countries are available. Detecting in real time a change in the typical pattern of trade and identifying countries where this change takes place is an important problem. This project will provide statistical methods that will allow making decisions about an emergence of an atypical pattern in a complex system in real time with certain theoretical guarantees. The project will also offer multiple interdisciplinary training opportunities for the next generation of statisticians and data scientists.

The methodology that will be developed is related to sequential change point detection, but is different because the in-control state is estimated rather than assumed. This requires new theoretical developments because it deals with complex infinite dimensional systems, whereas existing mathematical tools apply only to finite-dimensional systems. Panels of structured functions will be considered and methods for on-line identification of components undergoing change will be devised. All methods will be inferential with controlled probabilities of type I errors. Some of the key aspects of the project can be summarized in the following points. First, statistical theory leading to change point monitoring schemes in infinite dimensional function spaces will be developed. Second, strong approximations valid in Banach spaces will lead to assumptions not encountered in scalar settings and potentially to different threshold functions. Third, for monitoring of random density functions, the above challenges will be addressed in custom metric spaces. Fourth, since random densities are not observable, the effect of estimation will be incorporated. The new methodology will be applied to viral load measurements, investment portfolios, and global trade data.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." diff --git a/Topology/Awards-Topology-2024.csv b/Topology/Awards-Topology-2024.csv index 1f3ae27..6efa7d8 100644 --- a/Topology/Awards-Topology-2024.csv +++ b/Topology/Awards-Topology-2024.csv @@ -1,7 +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" -"2404810","Four-manifold Topology and Knotting in Dimensions 3--5","DMS","TOPOLOGY","09/01/2024","05/01/2024","Maggie Miller","TX","University of Texas at Austin","Continuing Grant","Swatee Naik","08/31/2027","$77,419.00","","maggie.miller@utexas.edu","110 INNER CAMPUS DR","AUSTIN","TX","787121139","5124716424","MPS","126700","","$0.00","Topology is the study of objects up to continuous deformations such as stretching and twisting. A common object of study is a knot, which a tangled loop in 3-dimensional space. Analogously, we may study knotted surfaces in a four-dimensional space, knotted three-dimensional objects in a five-dimensional space, and so forth. The study of knots in general dimension has applications to other areas of science such as biology, condensed matter physics, cryptography, and data analysis. One can study an object by investigating the possible behavior of knotted objects contained within. This project deals with ""low-dimensional"" topology, where the ambient space is of dimension at most five. Themes include exploring the difference between smooth and continuous equivalences of knotted objects, which typically involves different methods than in higher dimension. A key objective is to develop new tools and constructions applicable to low-dimensional topology. This project will additionally provide research opportunities for undergraduate and graduate students in mathematics.

This project will utilize constructive techniques from 3-, 4-, and 5-dimensional topology to study geometric questions involving knots and knotted surfaces in 3- and 4-manifolds. The PI will expand current understanding of knotted surfaces by using higher dimensional methods from surgery theory restricted to 4-dimensional cross-sections or by studying restrictions on 3-dimensional boundary and applying lower-dimensional techniques such as tools from knot Floer or Khovanov homology. Specific goals include understanding exotic phenomena in the 4-ball and 4-sphere, developing new concordance obstructions for surfaces in 4-manifolds, and extending structures such as fibrations from 3-manifolds over suitable bounded 4-manifolds.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2350250","Conference: Quantum Topology, Quantum Information and connections to Mathematical Physics","DMS","TOPOLOGY","05/01/2024","01/29/2024","Tian Yang","TX","Texas A&M University","Standard Grant","Eriko Hironaka","04/30/2025","$40,000.00","Sherry Gong, Zhizhang Xie, Michael Willis","tianyang@math.tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","126700","7556","$0.00","This award will provide financial support for a conference on Quantum Topology, Quantum Information, and Mathematical Physics, to be held from May 27 to 31, 2024, at Texas A&M University. The conference will bring together students and researchers interested in recent advances and new connections between the fields of quantum topology and quantum information theory and their applications to several branches of mathematics and physics, including low-dimensional topology, non-commutative geometry, operator algebra, representation theory, complexity theory, and quantum statistical physics. Participants will be split evenly between early career and established mathematicians, and the former group will receive priority for funding from this grant. Leading experts in the various topics will present the state of art in the subject in a way that is accessible to researchers at various career stages and emphasize new research directions and collaborations.

Quantum topology deals with interactions between low-dimensional topology, the theory of quantum groups, category theory, C*-algebra theory, gauge theory, conformal and topological field theory and statistical mechanics, while quantum information and computation theory brings together ideas from classical information theory, quantum mechanics and computer science and explores how the quantum mechanical properties of physical systems can be harnessed to achieve efficient data storage and transmission, and rapid computations. The interplay between these ideas and potential new advances and applications will be the main focus of the conference. More information can be found at the conference website: https://sites.google.com/tamu.edu/qtqimp/home.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"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." +"2350370","Conference: CMND 2024 program: Field Theory and Topology","DMS","INFRASTRUCTURE PROGRAM, TOPOLOGY","05/01/2024","01/18/2024","Pavel Mnev","IN","University of Notre Dame","Standard Grant","Qun Li","04/30/2025","$39,360.00","Stephan Stolz, Christopher Schommer-Pries","Pavel.N.Mnev.1@nd.edu","940 GRACE HALL","NOTRE DAME","IN","465565708","5746317432","MPS","126000, 126700","7556","$0.00","The program ?Field theory and topology? to be held at the Center for Mathematics at Notre Dame (CMND), June 3?21, 2024 will continue the line of CMND summer programs and consists of a graduate/postdoctoral summer school, a conference, and an undergraduate summer school. The program will expose a new generation of undergraduates and early-career researchers to the new ideas, developments, and open problems in the exciting meeting place between topology and quantum field theory where many surprising advances were made recently.

There is a rich interplay between quantum field theory and topology. The program ?Field theory and Topology? will focus on recent extraordinary developments in this interplay -- new invariants of manifolds and knots coming from field-theoretic constructions; new languages and paradigms for field theory coming from interaction with topology: functorial field theory, cohomological (Batalin-Vilkovisky) approach, approach via derived geometry and via factorization algebras. Among subjects discussed at the program will also be supersymmetric and extended topological field theories, holomorphic twists. Webpage of the event: https://sites.nd.edu/2024cmndthematicprogram/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2405453","Toward a dynamical theory of Thurston's norm","DMS","TOPOLOGY","09/01/2024","08/23/2024","Michael Landry","MO","Saint Louis University","Standard Grant","Eriko Hironaka","08/31/2027","$198,560.00","","michael.landry@slu.edu","221 N GRAND BLVD","SAINT LOUIS","MO","631032006","3149773925","MPS","126700","","$0.00","Spaces are often better understood by cutting them into pieces of lower dimension. For example, on a topographical map of a mountainous area, the 1-dimensional lines of constant altitude provide valuable information about a landscape. The breaks in the smooth pattern of contour lines indicate significant locations---high points, low points, and mountain passes. Moreover, the lines tell us how water will flow over the landscape. The pattern formed by these lines is known in mathematics as a ""foliation,"" and the paths taken by water determine a ""flow."" This project focuses on flows associated to foliations, but in one dimension higher than the map example: the foliations are comprised of 2-dimensional pieces inside a 3-dimensional space, similar to the universe in which we live. The PI will address longstanding open questions relating the fields of geometry, topology, and dynamics in 3-dimensions. In addition to original research, this project will involve the training of graduate students and support a mathematics periodical run by undergraduates and faculty at the PI's institution.

The project's overarching goal is to better understand the relationship between taut foliations and pseudo-Anosov flows in 3-manifolds, and to leverage this relationship to better understand the structure of the Thurston norm. A first concrete goal is to prove, with C.C. Tsang, a strengthening of a famous unpublished theorem of Gabai and Mosher: every taut finite depth foliation of a compact, irreducible, atoroidal 3-manifold is almost transverse to a pseudo-Anosov flow. The strengthening consists of characterizing when the construction yields a pseudo-Anosov flow ?without perfect fits,? a property relevant to the study of the Thurston norm. A second goal builds on the first, and is to relate the collection of pseudo-Anosov flows almost transverse to a given taut finite depth foliation to the collection of universal circles for that foliation. The PI aims to link these two families using the Gabai-Mosher construction, giving an approach to Mosher's Transverse Finiteness 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." +"2427220","Computations in Classical and Motivic Stable Homotopy Theory","DMS","TOPOLOGY","04/01/2024","04/09/2024","Eva Belmont","OH","Case Western Reserve University","Standard Grant","Swatee Naik","06/30/2025","$106,619.00","","eva.belmont@case.edu","10900 EUCLID AVE","CLEVELAND","OH","441061712","2163684510","MPS","126700","","$0.00","Algebraic topology is a field of mathematics that involves using algebra and category theory to study properties of geometric objects that do not change when those objects are deformed. A central challenge is to classify all maps from spheres to other spheres, where two maps are considered equivalent if one can be deformed to the other. The equivalence classes of these maps are called the homotopy groups of spheres, and collectively they form one of the deepest and most central objects in the field. Historically, much important theory has arisen out of attempts to compute more homotopy groups of spheres and understand patterns within them. This project involves furthering knowledge of the homotopy groups of spheres, using old and new techniques as well as computer calculations. The project also involves studying an analogue of these groups in algebraic geometry; this falls under a relatively new and actively developed area called motivic homotopy theory, which applies techniques in algebraic topology to study algebraic geometry. The broader impacts of this project center around supporting the local mathematics community through mentoring and promoting diversity. The principal investigator will help build the nascent homotopy theory community at the university and promote women and minorities in the subject through seminar organization and mentoring.

One of the main planned projects is a large-scale effort to compute the homotopy groups of spheres at the prime 3 in a range, using old and new techniques such as the Adams-Novikov spectral sequence as well as infinite descent machinery. This work will be aided by computer calculations, which short-circuits some of the technical difficulties encountered in previous attempts. Another main group of projects concerns computing the analogue of the stable homotopy groups of spheres in the world of R-motivic homotopy theory. This represents a continuation of prior work of the PI and collaborator; the plan is to supplement the techniques used in that work with computer calculations and a new tool, the slice spectral sequence. A third project concerns theory and spectral sequence computations aimed at computing the cohomology of profinite groups such as special linear groups and Morava stabilizer groups.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2341204","Conference: Midwest Topology Seminar","DMS","TOPOLOGY","02/01/2024","01/19/2024","Mark Behrens","IN","University of Notre Dame","Standard Grant","Eriko Hironaka","01/31/2025","$49,500.00","Daniel Isaksen, Vesna Stojanoska, Manuel Rivera, Carmen Rovi","mbehren1@nd.edu","940 GRACE HALL","NOTRE DAME","IN","465565708","5746317432","MPS","126700","7556","$0.00","This NSF award supports the Midwest Topology Seminar, from 2023 to 2026, a continuation of a previously supported regional conference series in algebraic topology that meets three times per year and rotates between universities in the Midwest and Great Lakes areas. The next two meetings are at Loyola University (March 2024) and Indiana University (Spring 2024). The Midwest Topology Seminar has been running continuously since the early 1970s, with at least one of the yearly meetings held in Chicago, the hub of the network, and is a long-standing, reliable, low-key, and low-cost way for participants to keep up with the field. The audiences are always large and diversified, drawing faculty and graduate students from a broad range of institutions. The Midwest Topology Seminar serves as a nexus for a vibrant community of research mathematicians, optimizing the distribution of new ideas through the field, especially among early career research mathematicians and mathematicians away from the traditional centers of research.

The Midwest is a traditional and continuing center of algebraic topology; hence there is a strong source of local speakers. Programs are augmented with featured speakers from around the country. Algebraic topology has always been broadly construed to include homotopy theory, algebraic K-theory, geometric group theory, and high dimensional manifolds; more recently the series has explored connections to algebraic geometry, representation theory, number theory, low dimensional manifolds, and mathematical physics. Financial support will go to graduate students and research mathematicians with limited funds from other sources. The conference web site is http://www.rrb.wayne.edu/MTS/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2404843","Curve counting beyond rational numbers","DMS","TOPOLOGY","08/15/2024","08/15/2024","Shaoyun Bai","MA","Massachusetts Institute of Technology","Standard Grant","Swatee Naik","07/31/2027","$183,897.00","","shaoyunb@mit.edu","77 MASSACHUSETTS AVE","CAMBRIDGE","MA","021394301","6172531000","MPS","126700","","$0.00","This project focuses on symplectic manifolds, which are crucial objects in understanding the mathematics behind many physical phenomena, such as the movement of planets and the behavior of particles. The main goal is to find different ways to identify and count surfaces within these spaces. Understanding these two-dimensional objects can help us comprehend the more abstract, high-dimensional spaces they exist in. By analyzing this detailed geometric information, the project aims to tackle theoretical mathematical problems inspired by physics, such as those seen in Hamiltonian mechanics and string theory. Solving these theoretical problems can enhance our understanding of complex systems, potentially resulting in advancements in technology, healthcare, and general knowledge of nature. In addition, this project will provide research training opportunities for students.

The counts of pseudo-holomorphic maps into symplectic manifolds are usually rational-valued due to the presence of nontrivial automorphisms. The project aims to answer questions in Hamiltonian dynamics and mathematical physics by developing curve counts with coefficients beyond rational numbers, including integers, complex K-theory, and complex cobordism. New curve-counting invariants inspired by cohomological operations and homotopy-theoretic enhancement of Floer theory will be developed along the way. The research topics include global Kuranishi charts for operations in the integral Hamiltonian Floer theory, Adams operations in enumerative geometry, Floer homotopy types over complex cobordism, and the study of periodic points of Hamiltonian diffeomorphisms.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2350250","Conference: Quantum Topology, Quantum Information and connections to Mathematical Physics","DMS","TOPOLOGY","05/01/2024","01/29/2024","Tian Yang","TX","Texas A&M University","Standard Grant","Eriko Hironaka","04/30/2025","$40,000.00","Sherry Gong, Zhizhang Xie, Michael Willis","tianyang@math.tamu.edu","400 HARVEY MITCHELL PKY S STE 30","COLLEGE STATION","TX","778454375","9798626777","MPS","126700","7556","$0.00","This award will provide financial support for a conference on Quantum Topology, Quantum Information, and Mathematical Physics, to be held from May 27 to 31, 2024, at Texas A&M University. The conference will bring together students and researchers interested in recent advances and new connections between the fields of quantum topology and quantum information theory and their applications to several branches of mathematics and physics, including low-dimensional topology, non-commutative geometry, operator algebra, representation theory, complexity theory, and quantum statistical physics. Participants will be split evenly between early career and established mathematicians, and the former group will receive priority for funding from this grant. Leading experts in the various topics will present the state of art in the subject in a way that is accessible to researchers at various career stages and emphasize new research directions and collaborations.

Quantum topology deals with interactions between low-dimensional topology, the theory of quantum groups, category theory, C*-algebra theory, gauge theory, conformal and topological field theory and statistical mechanics, while quantum information and computation theory brings together ideas from classical information theory, quantum mechanics and computer science and explores how the quantum mechanical properties of physical systems can be harnessed to achieve efficient data storage and transmission, and rapid computations. The interplay between these ideas and potential new advances and applications will be the main focus of the conference. More information can be found at the conference website: https://sites.google.com/tamu.edu/qtqimp/home.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2404810","Four-manifold Topology and Knotting in Dimensions 3--5","DMS","TOPOLOGY","09/01/2024","05/01/2024","Maggie Miller","TX","University of Texas at Austin","Continuing Grant","Swatee Naik","08/31/2027","$77,419.00","","maggie.miller@utexas.edu","110 INNER CAMPUS DR","AUSTIN","TX","787121139","5124716424","MPS","126700","","$0.00","Topology is the study of objects up to continuous deformations such as stretching and twisting. A common object of study is a knot, which a tangled loop in 3-dimensional space. Analogously, we may study knotted surfaces in a four-dimensional space, knotted three-dimensional objects in a five-dimensional space, and so forth. The study of knots in general dimension has applications to other areas of science such as biology, condensed matter physics, cryptography, and data analysis. One can study an object by investigating the possible behavior of knotted objects contained within. This project deals with ""low-dimensional"" topology, where the ambient space is of dimension at most five. Themes include exploring the difference between smooth and continuous equivalences of knotted objects, which typically involves different methods than in higher dimension. A key objective is to develop new tools and constructions applicable to low-dimensional topology. This project will additionally provide research opportunities for undergraduate and graduate students in mathematics.

This project will utilize constructive techniques from 3-, 4-, and 5-dimensional topology to study geometric questions involving knots and knotted surfaces in 3- and 4-manifolds. The PI will expand current understanding of knotted surfaces by using higher dimensional methods from surgery theory restricted to 4-dimensional cross-sections or by studying restrictions on 3-dimensional boundary and applying lower-dimensional techniques such as tools from knot Floer or Khovanov homology. Specific goals include understanding exotic phenomena in the 4-ball and 4-sphere, developing new concordance obstructions for surfaces in 4-manifolds, and extending structures such as fibrations from 3-manifolds over suitable bounded 4-manifolds.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350344","Collaborative Research: Conference: Trisections Workshops: Connections with Knotted Surfaces and Diffeomorphisms","DMS","TOPOLOGY","05/01/2024","02/13/2024","Maggie Miller","TX","University of Texas at Austin","Standard Grant","Eriko Hironaka","04/30/2026","$49,382.00","","maggie.miller@utexas.edu","110 INNER CAMPUS DR","AUSTIN","TX","787121139","5124716424","MPS","126700","7556","$0.00","This proposal will fund the ?Trisections Workshop: Connections with Knotted Surfaces,? which will take place at the University of Nebraska-Lincoln from June 24-28, 2024, and the ?Trisections Workshop: Connections with Diffeomorphisms,? which will take place at the University of Texas at Austin during one week in the summer of 2025. Workshop attendees will include established experts, early-career researchers, and students, and the program will actively engage all participants. Each morning will feature plenary talks by experts and/or lightning talks highlighting the work of junior researchers. The afternoons will be devoted to working in groups on open problems. This series of regular workshops has been critical to the development of an enthusiastic community of researchers in low-dimensional topology, helping this new and growing area gain momentum and fostering numerous collaborations across career stages and demographics. The organizers take pride in the camaraderie and welcoming atmosphere they strive to create, and many in the community deeply value and appreciate these events.

A trisection splits a 4-dimensional space into three simple pieces. Since their introduction roughly a decade ago, trisections have proven to be a successful new tool with which to study smooth 4-manifolds, with numerous articles written in the interim to develop the foundations for trisection theory. An important strength of the theory of trisections is the way it interfaces with a variety of other topics in low-dimensional topology. This interface provides an opportunity to explore many classical areas of 4-manifold topology through a new lens. Such areas include, for example, the study of knotted surfaces in 4-space, diffeomorphisms of 4-manifolds, exotic smooth structures, group actions and (branched) covering spaces, and symplectic structures. The main goal of these workshops is to bring together researchers from multiple areas to propose and to work on open problems, with a particular focus on the inclusion of early career researchers. The workshops are preceded by a series of introductory virtual pre-workshop talks, which serve to bring new researchers up to speed, to facilitate the work to be done in groups, and to incorporate a broader, worldwide audience. The website for the 2024 workshop can be found here: https://sites.google.com/view/tw2024.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405061","Geometric and spectral structure of group automorphisms and extensions","DMS","TOPOLOGY","09/01/2024","08/07/2024","Spencer Dowdall","TN","Vanderbilt University","Standard Grant","Eriko Hironaka","08/31/2027","$270,578.00","","spencer.dowdall@vanderbilt.edu","110 21ST AVE S","NASHVILLE","TN","372032416","6153222631","MPS","126700","","$0.00","This project will probe fundamental geometric and dynamical phenomena in several mathematical contexts centered around the notion of symmetry. Mathematically, symmetry (as can appear in molecules and in rigid motions of space) is formalized in the construct of a group, a foundational concept in many branches of mathematics. This project focuses on groups that arise in the study of low-dimensional topology and geometry that concern both the structure of the space itself, such as its curvature, distance and volume, and the structure of their associated parameter spaces, which capture the geometric structures supported on the space, or the configurations of points on the space. For the purposes of this project, the two most important classes of examples are graphs and surfaces, and the groups that that can be obtained by combining these objects in basic ways. This project will identify and study how the inherent structure of these groups reveals important geometric and dynamical phenomena. The research activities in this project will be integrated with graduate and postdoctoral training and the development of structured avenues for undergraduate students to engage in mathematical experimentation and exploration.

Specifically, this project investigates the geometry of groups and the dynamics of free group automorphisms. There are several distinct but interrelated goals: Firstly, the project will develop a new theory of geometric finiteness for subgroups of mapping class groups that is tested against examples and understood from the dual perspectives of the intrinsic geometry of surface group extensions and the extrinsic structure of mapping class groups. This is motivated by the theory of Kleinian groups and builds on the PI's recent work in studying surface group extensions associated to lattice Veech groups. Secondly, the project will study the asymptotic behavior of least pseudo-Anosov dilatations and prove that, up to normalization, these numbers accumulate on only finitely many values. This will be accomplished by carefully analyzing the fibrations of individual hyperbolic 3-manifolds and using the fact that all least dilatation pseudo-Anosovs arise as monodromies of only finitely many 3-manifolds. Thirdly, the project will further develop a new theory of orientability of fully irreducible free group automorphisms and study how this interacts with branched covers, stretch factors in finite covers, and polynomial invariants of free-by-cyclic groups. In particular, it will utilize train track theory to show that each fully irreducible automorphism has a canonical orientation double cover. Fourthly, the project will study the Cannon-Thurston maps that encode the boundary structure of hyperbolic group extensions and prove that these maps are uniformly finite-to-one.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405046","Hyperbolic manifolds and groups","DMS","TOPOLOGY","08/15/2024","08/09/2024","David Futer","PA","Temple University","Standard Grant","Eriko Hironaka","07/31/2027","$300,000.00","","dfuter@temple.edu","1805 N BROAD ST","PHILADELPHIA","PA","191226104","2157077547","MPS","126700","","$0.00","A 3-manifold is a space where an object can move around in three distinct perpendicular directions. The universe is a three-manifold whose global structure is not yet understand. Thanks to transformative work around the turn of the century, it is known that the geometry of a manifold (measurements of angles, distances, and curvature) is closely tied to its large-scale structure. What is missing at this point is a quantitative understanding of how geometry and large-scale topology determine one another. This project seeks quantitative information of this nature. The project includes problems pursued in collaboration with current and recent graduate students mentored by the PI. The project also supports the PI?s leadership efforts in building stronger mentoring in his department, nurturing the mathematical community in the Philadelphia area, and training junior mathematicians through a national graduate conference.

Mathematically, this project seeks to make progress on several important open questions about hyperbolic 3-manifolds and their fundamental groups, with emphasis on effective computation and large-scale structure. One question involves quantitative control on the change in geometry under Dehn surgery, including applications to the cosmetic surgery conjecture that are coded into software for the mathematical community. The second question involves identifying the Margulis constant and understanding the structure of Kleinian groups generated by two short elements. The third question involves relationships between the rank and genus of 3-manifolds. The fourth question involves a coarse understanding of the fixed-point properties of pseudo-Anosov maps on surfaces, with applications to invariants of knots and 3-manifolds. The fifth question involves a quantitative understanding of special covers of 3-manifolds.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -10,8 +15,8 @@ "2405271","The geometry of moduli spaces from low-dimensional topology and applications","DMS","TOPOLOGY","08/15/2024","08/02/2024","Boyu Zhang","MD","University of Maryland, College Park","Standard Grant","Swatee Naik","07/31/2027","$177,469.00","","bzh@umd.edu","3112 LEE BUILDING","COLLEGE PARK","MD","207425100","3014056269","MPS","126700","","$0.00","Low Dimensional Topology is a branch of mathematics that studies shapes of three and four-dimensional objects. This project explores such objects using tools inspired by modern physics. One such tool is the Yang-Mills equation, used in quantum field theory to describe electro-weak interactions. Solutions to the Yang-Mills equation on a manifold can reveal deep insights into the underlying topology. The construction of configuration spaces on manifolds is inspired by Feynman diagrams; it has recently been used to answer long-standing open problems in low-dimensional topology. These ideas also interact closely with many other areas of mathematics, such as non-linear partial differential equations, algebraic topology, and algebraic geometry. The PI will use the existing tools in gauge theory and configuration space theory to study questions in three- and four-dimensional topology and develop new tools in this field by working on fundamental analytical questions about gauge-theoretic equations. During the project, the PI will train graduate and undergraduate students, organize high school educational activities, and participate in outreach programs to attract more students to mathematics.

The research activities of this project will focus on the following three major directions. The first direction studies the higher algebraic structures in instanton Floer homology and its relations with gluings of 3-manifolds. The second direction studies the analytic properties of generalized Seiberg?Witten equations. The third direction explores the applications of Kontsevich configuration space integrals in 4-dimensional topology and uses it to study smooth mapping class groups in dimension 4.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405033","Boundaries and subgroup structure","DMS","TOPOLOGY","08/15/2024","08/02/2024","Genevieve Walsh","MA","Tufts University","Standard Grant","Eriko Hironaka","07/31/2027","$249,648.00","","genevieve.walsh@tufts.edu","169 HOLLAND ST","SOMERVILLE","MA","021442401","6176273696","MPS","126700","","$0.00","This project addresses a key problem in the field of geometric group theory: to understand the relation between geometric and algebraic structures and properties of a group. Research in this area has motivation coming from mathematical theory as well as from applications in cryptography and algorithms. In this project, the PI will investigate groups endowed with a geometric structure, and study situations when such a group can have subgroups that are geometrically ill-behaved, for example, having the property of being geometrically infinite. The PI will also engage in several projects aimed at broadening participation in mathematics by providing resources and creating an environment that supports and welcomes under-represented populations into mathematics. This will include giving expository lecture series, advocating for equity in publishing, organizing conferences and participating in the Tufts University Prison Initiative, seeking ways to improve their math training program for incarcerated and formerly incarcerated people.

The PI will investigate the relation between three important topics in the theory of hyperbolic and relatively hyperbolic groups. The first is the boundary of a hyperbolic group. This is a canonical topological object that carries a lot, but not complete, group theoretical information about the group. The second is the quasi-isometry type of a group. Many properties are invariant under quasi-isometry, in particular the boundary. The third is the subgroup structure of groups whose finitely generated subgroups are not necessarily quasi-convex. Very little is known about this outside of hyperbolic 3-manifold groups, and the PI is pushing this to other classes of groups.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2401587","Polylogarithms, cluster algebras, and hyperbolic geometry","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","08/15/2024","08/02/2024","Christian Zickert","MD","University of Maryland, College Park","Standard Grant","Tim Hodges","07/31/2027","$210,000.00","","zickert@umd.edu","3112 LEE BUILDING","COLLEGE PARK","MD","207425100","3014056269","MPS","126400, 126700","","$0.00","This award supports research on the interplay between three different research areas: polylogarithms, cluster algebras, and hyperbolic geometry. Polylogarithms generalize the natural logarithm and have been studied since the 18th century. Cluster algebras, invented in the early 21st century, are purely combinatorial objects which are widely studied and broadly applicable. Hyperbolic geometry is a geometry with constant negative curvature, where Euclid's fifth postulate fails. Recent advances have revealed surprising links between these areas. For example, formulas for scattering amplitudes in high energy physics frequently involve polylogarithms evaluated at cluster algebra coordinates. Also, the volume of a certain hyperbolic polyhedron known as an orthoscheme, where successive faces form right angles, is given by a polylogarithm formula. The proposal will investigate key conjectures, find new examples of hyperbolic manifolds, and compute invariants using cluster coordinates. The PI will involve both graduate and undergraduate students in this project and continue his outreach to local schools.

The proposal will explore the relationship between polylogarithms and cluster algebras focusing on several key conjectures in the field. These include the Matveiakin-Rudenko conjecture, that all polylogarithm relations arise from the cluster polylogarithm relations of type A_n; Zagier's polylogarithm conjecture, that the zeta function of a number field at integers is expressed by polylogarithms; and Goncharov's depth conjecture, that a polylogarithm is a classical polylogarithm if an only if its truncated coproduct vanishes. The proposal will explore special cases of these conjectures using Matveiakin and Rudenko's notion of cluster polylogarithms as well as new tools developed by the PI and his collaborators. In addition, the proposal will study Rudenko's polylogarithm formula for a hyperbolic orthoscheme, find new examples of hyperbolic manifolds that don't arise from Coxeter groups (and therefore have dihedral angles that are not a submultiple of pi), and generalize formulas for Cheeger-Chern-Simons invariants from dimension 3 to dimension 5.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2405244","Geometric limits in low dimensional geometry and topology","DMS","TOPOLOGY","08/01/2024","07/31/2024","Ian Biringer","MA","Boston College","Standard Grant","Eriko Hironaka","07/31/2027","$260,000.00","","ianbiringer@gmail.com","140 COMMONWEALTH AVE","CHESTNUT HILL","MA","024673800","6175528000","MPS","126700","","$0.00","The central theme of this project is that certain classes of mathematical shapes can be understood better by analyzing other shapes that they approximate. For instance, a sphere with a very large radius, like the earth, approximates a flat plane from the perspective of a person standing upon it. Planar geometry then informs the study of spherical geometry. The particular shapes considered in this project are `hyperbolic manifolds', which have been among the most important objects in theoretical geometry for the past hundred years. To supplement the research component of the project, the PI will continue to develop inquiry-based learning (IBL) courses at Boston College, will revise and disseminate his online book `Geometry in 2 dimensions', and run learning workshops for early career mathematicians.

In low dimensional geometry and topology, one often studies a sequence of Riemannian manifolds by passing to an appropriate `geometric limit' manifold. For instance, this technique is essential in Thurston's program to understand 3-dimensional manifolds via hyperbolic geometry, and in the proof of his Geometrization Conjecture by Perelman in 2003. This current project is centered on the structure and applications of geometric limits, especially in hyperbolic geometry. Specifically, the PI will study the global topology of the associated `space of all hyperbolic manifolds', continuing his previous work with Lazarovich-Leitner and Warakkagun, and will use geometric limits and their probabilistic cousins `Benjamini-Schramm limits' to study the relationship between the `rank' of a closed hyperbolic 3-manifold and its geometry, extending his previous work with Souto and Abert et al.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2404828","Computational structures in equivariant chromatic homotopy theory","DMS","TOPOLOGY","08/15/2024","08/02/2024","XiaoLin Danny Shi","WA","University of Washington","Standard Grant","Eriko Hironaka","07/31/2027","$217,000.00","","dannyshi@uw.edu","4333 BROOKLYN AVE NE","SEATTLE","WA","981951016","2065434043","MPS","126700","","$0.00","Spheres are among the simplest geometric objects, serving as building blocks for more complicated topological spaces. The homotopy groups of spheres (collections of continuous functions between spheres, considered up to certain deformations groups) hold fundamental information about maps between topological spaces and have deep connections to number theory, algebraic geometry, differential topology, and geometric topology. Despite their ease of definition, there are few effective methods to compute homotopy groups of spheres. Using equivariant technology the PI will explore the rich connections between equivariant homotopy theory and chromatic homotopy theory and use them to develop powerful new computational techniques. This research will be integrated with conference organization, and graduate students and postdocs mentoring and training. The PI will also be engaged in outreach to local middle school teachers and students.

The research involves a range of projects that will leverage recent discoveries in equivariant homotopy theory to advance computations in chromatic homotopy theory. The study of Lubin-Tate theories is one of the most important areas of research in chromatic homotopy theory. In 2009, Hill?Hopkins?Ravenel's resolution of the Kervaire invariant problem elevated equivariant homotopy theory as a potent tool to drive significant progress in chromatic homotopy theory and address classical problems in geometry and topology. The projects involve exploring computational structures in the equivariant slice spectral sequences of Real bordism theories and Lubin-Tate theories at the prime 2. This endeavor extends to achieving analogous results at odd primes. To achieve these goals, the PI plans to employ new equivariant techniques, including transchromatic isomorphisms, stratification results, and the generalized Tate diagram of spectral sequences. These methods will enable extensive equivariant chromatic computations, establish general differential patterns, and reveal a broader range of transchromatic phenomena in the equivariant slice spectral sequences of norms of Real bordism theories and Lubin-Tate theories across various groups and heights.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2405244","Geometric limits in low dimensional geometry and topology","DMS","TOPOLOGY","08/01/2024","07/31/2024","Ian Biringer","MA","Boston College","Standard Grant","Eriko Hironaka","07/31/2027","$260,000.00","","ianbiringer@gmail.com","140 COMMONWEALTH AVE","CHESTNUT HILL","MA","024673800","6175528000","MPS","126700","","$0.00","The central theme of this project is that certain classes of mathematical shapes can be understood better by analyzing other shapes that they approximate. For instance, a sphere with a very large radius, like the earth, approximates a flat plane from the perspective of a person standing upon it. Planar geometry then informs the study of spherical geometry. The particular shapes considered in this project are `hyperbolic manifolds', which have been among the most important objects in theoretical geometry for the past hundred years. To supplement the research component of the project, the PI will continue to develop inquiry-based learning (IBL) courses at Boston College, will revise and disseminate his online book `Geometry in 2 dimensions', and run learning workshops for early career mathematicians.

In low dimensional geometry and topology, one often studies a sequence of Riemannian manifolds by passing to an appropriate `geometric limit' manifold. For instance, this technique is essential in Thurston's program to understand 3-dimensional manifolds via hyperbolic geometry, and in the proof of his Geometrization Conjecture by Perelman in 2003. This current project is centered on the structure and applications of geometric limits, especially in hyperbolic geometry. Specifically, the PI will study the global topology of the associated `space of all hyperbolic manifolds', continuing his previous work with Lazarovich-Leitner and Warakkagun, and will use geometric limits and their probabilistic cousins `Benjamini-Schramm limits' to study the relationship between the `rank' of a closed hyperbolic 3-manifold and its geometry, extending his previous work with Souto and Abert et al.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350002","Quantum Topology Beyond Semi-Simplicity","DMS","TOPOLOGY","08/15/2024","08/02/2024","Nathan Geer","UT","Utah State University","Standard Grant","Swatee Naik","07/31/2027","$299,996.00","","nathan.geer@usu.edu","1000 OLD MAIN HL","LOGAN","UT","843221000","4357971226","MPS","126700","","$0.00","Physics-inspired mathematics has effectively laid the foundation and provided the terminology for the most advanced areas of modern physics. This project aims to create new algebraic and geometric tools to help formulate ideas and methods of quantum physics in a precise mathematical way. Low-dimensional topology is an area of mathematics that studies three and four dimensional spaces. Theory of quantum groups has been productively used in low-dimensional topology, particularly with the creation of quantum invariants. Within this context, the Principal Investigator (PI) and his collaborators have developed new systematic strategies. The focus of this project is to further investigate and develop these strategies, aiming to exploit the powerful properties of the ?renormalized? quantum invariants in several areas of mathematics. The unique attributes of this work open the door to novel research avenues in algebra, topology, geometry, and mathematical physics. The broader impacts are through STEM education, mentoring, and outreach. The PI will advise graduate students and postdocs on projects related to the main objectives of the project. The PI has co-organized many conferences and will continue such outreach activities to develop communication and collaborative research with other mathematicians, as well as to foster broader applications of the work supported by this award.

The past thirty years have witnessed a transformative influx of quantum field theory into low-dimensional topology, leading to a novel perspective on link and three-manifold invariants. The discovery of the Jones polynomial by V. Jones in 1984 and its interpretation through three-dimensional quantum field theory by E. Witten in 1989 have paved the way for the application of new algebraic methods to study topology. These advancements have given rise to a new field of mathematics known as ""quantum topology?. Most of the theory of quantum invariants involves monoidal categories with certain additional properties, such as being semi-simple. The PI and his collaborators have created a theory of re-normalized quantum invariants (RQIs) of low-dimensional manifolds arising from categories that are not semi-simple. The RQIs have their own unique features and provide mathematical interpretations of Topological Quantum Field Theories (TQFTs) with categories of line operators that are non-semi-simple; furthermore, the RQIs are more powerful than their standard counterparts. This project will explore the nature and physical meaning of the re-normalized Reshetikhin-Turaev three-manifold invariants and their associated TQFTs via certain classes of examples appearing in the context of Chern-Simons theory and vertex operator algebras. It also proposes to enhance and generalize recently defined non-compact skein TQFTs.

This award reflects 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." "2430432","Conference: Kylerec Student Workshops in Symplectic and Contact Geometry","DMS","TOPOLOGY","11/01/2024","08/01/2024","Eleny-Nicoleta Ionel","CA","Stanford University","Standard Grant","Qun Li","10/31/2027","$130,483.00","","ionel@math.stanford.edu","450 JANE STANFORD WAY","STANFORD","CA","943052004","6507232300","MPS","126700","7556","$0.00","The 2025 edition of the Kylerec Graduate Student Workshop is scheduled to take place during the period June 23-27, 2025, near Tahoe, CA, and this award provides support for the next three editions of the workshop (2025, 2026 and 2027). The Kylerec workshop aims to introduce aspiring mathematicians in the fields of symplectic and contact geometry and from many institutions to vibrant areas of research, fostering collaboration, forming strong research ties between young researchers, and thus promoting future collaboration and research. The workshop is specifically designed to encourage the development of a diverse group of researchers in the fields of symplectic and contact geometry. It is a week-long intensive workshop, in which all activities occur under one roof which serves as the mathematical and social center for the week. The lectures are delivered by the graduate student participants with the help of three or four mentors, who are early career researchers and emerging experts in the field. This setup enhances communication skills, encourages active involvement of the participants and forging new collaborations. Participants also cook, clean and eat together, further fostering the sense of community.

The planned topic for the 2025 Kylerec workshop is Floer homotopy theory, focusing on the emerging subject of lifting constructions in symplectic Floer theory to the level of stable homotopy theory, and applications to classical problems in symplectic geometry such as the classification of exact Lagrangian submanifolds or the study of Hamiltonian fibrations and families of symplectic manifolds. Ever since Floer's original breakthrough on the Arnold conjecture, constructions of Floer-type theories of increasing complexity were introduced with tremendous success for applications in symplectic topology, such as the recent Abouzaid?Blumberg result on the Arnold conjecture with mod p coefficients. The objective of the Kylerec workshop is to understand the current state of the art in these topics, including both the technical tools utilized and the applications, as well as some of the broader philosophy that has come out of the work on these topics. Along the way, we hope that participants will encounter a wide variety of different ideas coming from the various approaches, as well as exciting new areas and open problems stemming from the recent developments. Kylerec workshops website: https://kylerec.wordpress.com/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -19,9 +24,9 @@ "2401375","Collaborative Research: Small quantum groups, their categorifications and topological applications","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","07/15/2024","07/16/2024","Joshua Sussan","NY","CUNY Medgar Evers College","Standard Grant","Tim Hodges","06/30/2027","$201,860.00","","joshuasussan@gmail.com","1650 BEDFORD AVE","BROOKLYN","NY","112252017","7182706107","MPS","126400, 126700","","$0.00","This award funds research in an area of abstract algebra. Throughout history, mathematics and physics have had profound influences on each other. In the late 20th century, physicists discovered a deep connection between quantum physics and three-dimensional shapes, leading to the concept of topological quantum field theory (TQFT). While these 3D theories cannot fully describe our 4D universe, condensed matter physicists have found surprising applications of them in the field of quantum computing. In an effort to bridge the gap between these three-dimensional theories and our actual universe, Crane and Frenkel introduced a program called ""categorification"" in the late 1990s. This program aims to lift three-dimensional TQFTs to four dimensions, making it a more direct reflection of our physical reality. The PIs will involve students and postdocs in this research, with particular focus on students from underrepresented minorities.

The first significant development in categorification was the discovery of Khovanov homology. This is a powerful invariant of links whose graded Euler characteristic is the Jones polynomial. The investigators plan to use the technical machinery of hopfological algebra to extend a dual version of Khovanov homology to a homological invariant of three-dimensional manifolds whose graded Euler characteristic is the Witten-Reshetikhin-Turaev invariant. Ideally, this construction will be fully functorial, giving rise to an invariant of four-dimensional manifolds, while remaining computationally accessible. These invariants are expected be sensitive to smooth structures and should give insights into smooth topology not provided by gauge theoretic invariants like Donaldson and Seiberg-Witten invariants. This direction will build upon the investigators' previous work on categorified quantum groups and their representations at roots of unity. It is an open question of how to incorporate hopfological structures into Khovanov homology. This should lead to new homotopic notions. The investigators also plan on continuing to develop non-semisimple versions of three-dimensional topological quantum field theories with an eye toward applications to quantum computation. These non-semisimple invariants have certain topological advantages over their more classical semisimple counterparts. This line of research will also build upon their work on the centers of small quantum groups which has recently been an active area of research in geometric representation theory.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2400006","Conference: Underrepresented Students in Algebra and Topology Research Symposium (USTARS)","DMS","INFRASTRUCTURE PROGRAM, ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","03/15/2024","03/12/2024","Ryan Moruzzi","CA","California State University, East Bay Foundation, Inc.","Standard Grant","Adriana Salerno","02/28/2025","$36,000.00","Christopher ONeill, Robyn Brooks","ryan.moruzzi@csueastbay.edu","25800 CARLOS BEE BLVD","HAYWARD","CA","945423000","5108854212","MPS","126000, 126400, 126700","7556","$0.00","This award will support the Underrepresented Students in Topology and Algebra Research Symposium (USTARS). A goal of this conference is to highlight research being conducted by underrepresented students in the areas of algebra and topology. At this unique meeting, attendees are exposed to a greater variety of current research, ideas, and results in their areas of study and beyond. Participants are also given the opportunity to meet and network with underrepresented professors and students who may later become collaborators and colleagues. This is particularly important for students with great academic potential who do not attend top-tier research institutions; students that are often overlooked, despite a strong faculty and graduate student population. Furthermore, USTARS promotes diversity in the mathematical sciences by encouraging women and minorities to attend and give talks. Participants of USTARS continue to influence the next generation of students in positive ways by serving as much needed mentors and encouraging students in the mathematical sciences to advance themselves and participate in research and conference events. USTARS exposes all participants to the research and activities of underrepresented mathematicians, encouraging a more collaborative mathematics community.

The Underrepresented Students in Topology and Algebra Research Symposium (USTARS) is a project proposed by a group of underrepresented young mathematicians. The conference organizing committee is diverse in gender, ethnicity, and educational background, and is well-positioned to actively encourage participation by women and minorities. The symposium includes networking sessions along with research presentations. Speakers will give 30-minute parallel research talks. Graduate students will give at least 75% of these presentations. Two distinguished graduate students and one invited faculty member are chosen to give 1-hour presentations and a poster session featuring invited undergraduates is also planned. Additionally, a discussion panel and creative math session will provide networking, guidance, and mentorship opportunities from past USTARS participants that have transitioned to full-time faculty positions. The conference website is https://www.ustars.org/.

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

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

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405452","A Heegaard Floer theoretic approach to 4-dimensional genus questions","DMS","OFFICE OF MULTIDISCIPLINARY AC, TOPOLOGY","08/01/2024","07/24/2024","Katherine Raoux","AR","University of Arkansas","Standard Grant","Swatee Naik","07/31/2027","$149,156.00","","kraoux@uark.edu","1125 W MAPLE ST STE 316","FAYETTEVILLE","AR","727013124","4795753845","MPS","125300, 126700","9150","$0.00","Mathematical breakthroughs in the 20th century revealed that four-dimensional spaces are more mysterious than spaces in any other dimension. One of the best ways to study these spaces is to break them into smaller pieces and examine the knots and surfaces within. One way of distinguishing spaces is to determine surfaces of least complexity, for example, ?minimal genus?. This project focuses on minimal genus questions in a variety of contexts. The PI brings expertise in Heegaard Floer theory, which has proved effective at addressing these kinds of questions. As part of this project, the PI plans to organize a yearly colloquium and special lecture for the Association for Women in Mathematics Student Chapter at the University of Arkansas. Additionally, the PI will co-organize a regional conference in topology and geometry that serves the EPSCoR regions of Arkansas, Oklahoma, and beyond, and continue to lead the Math Olympiads for Elementary and Middle Schools (MOEMS) team at the Fayetteville Public Library.

Minimal genus problems are central to the study of low dimensional manifolds. The project addresses variations of the minimal genus problem and its broad implications. The PI will study the relationship between the knot concordance group and the homology cobordism group. The PI will address the existence of deep slice knots in contractible 4-manifolds. The PI will study an analog of the Thurston norm for knots in rational homology spheres. The PI will develop bordered Floer techniques to study knots that are not freely equivariantly slice. Finally, the PI will study minimal genus problems in the context of contact topology.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2404322","Conference: Young Geometric Group Theory XII","DMS","TOPOLOGY","04/15/2024","04/05/2024","Rylee Lyman","NJ","Rutgers University Newark","Standard Grant","Swatee Naik","03/31/2025","$35,000.00","","rylee.lyman@rutgers.edu","123 WASHINGTON ST","NEWARK","NJ","071023026","9739720283","MPS","126700","7556","$0.00","This award will provide partial support for U.S.-based participants in ?Young Geometric Group Theory XII?, a conference which will be held in Bristol, U.K. from April 8 to April 12, 2024. The Young Geometric Group Theory conference series is the largest annual conference in geometric group theory, and unique among similar events for being primarily aimed at graduate students and early career researchers. The purpose of the conference is to expose early career researchers to cutting edge research in the field, provide them opportunities to share their work, and to facilitate new collaborations. The conference includes mini-courses by established experts, plenary talks by selected senior and early career researchers, lighting talks and a poster session for participants, small-group informal discussions, and panel discussions, which will focus on career opportunities as well as equity, diversity and inclusion. Participating in a conference in this series may be transformative for a young researcher?s career, and NSF support makes attendance accessible for U.S.-based participants.

The mini-courses for this conference are Cubical Geometry by Mark Hagen, Convergence Groups, Three-Manifolds and Anosov-Like Actions by Kathryn Mann, and Analytic/Topological Obstructions to Coarse Embeddings by Romain Tessera. Each of these lectures, along with four senior plenary talks will present an overview of the topic and expose participants to tools and recent developments in the field. Additionally, four plenary talks by early career researchers will broaden the scope of the conference and present new developments in the field from researchers closer to the participants in career stage. More information can be found on the conference?s website: https://sites.google.com/view/yggt2024

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

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2342119","Conference: Riverside Workshop on Geometric Group Theory 2024","DMS","TOPOLOGY","04/01/2024","12/04/2023","Matthew Durham","CA","University of California-Riverside","Standard Grant","Qun Li","03/31/2025","$30,000.00","Thomas Koberda","mdurham@ucr.edu","200 UNIVERSTY OFC BUILDING","RIVERSIDE","CA","925210001","9518275535","MPS","126700","7556","$0.00","This award provides funding for the second Riverside Workshop on Geometric Group Theory, which is to be held May 3-6, 2024, at the University of California Riverside. This workshop will feature three minicourses given by early-career mathematicians working in the field of geometric group theory. This is an active area of research lying at the interface of geometry, algebra, and dynamical systems, with many applications especially to low-dimensional topology, and which has seen many break-through results over the past decades. The topic of each minicourse will be a cutting-edge technique or idea developed by the speaker, with an audience of graduate students and postdocs in mind. Each speaker will also produce an expository paper on the topic of their minicourse, and these papers will be compiled into a book, mirroring the 2023 version of the activity.

Much of the machinery in geometric group theory is highly technical, and so graduate students looking to enter the field will benefit from careful exposition of the big ideas of the field in lecture series that elaborate extensively on background and examples. The invited minicourse speakers are: Abdalrazzaq Zalloum (University of Toronto), who will speak on the geometry of CAT(0) and injective spaces; Emily Stark (Wesleyan University), who will speak on boundaries of groups; and Inhyeok Choi (Korea Institute for Advanced Study), who will speak on random walks on groups and their applications. The website of the workshop is https://sites.google.com/view/rivggt24/home.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2415445","CAREER: Machine learning, Mapping Spaces, and Obstruction Theoretic Methods in Topological Data Analysis","DMS","TOPOLOGY, CDS&E-MSS","04/01/2024","07/21/2024","Jose Perea","MA","Northeastern University","Continuing Grant","Jodi Mead","04/30/2025","$350,849.00","","j.pereabenitez@northeastern.edu","360 HUNTINGTON AVE","BOSTON","MA","021155005","6173733004","MPS","126700, 806900","079Z, 1045","$0.00","Data analysis can be described as the dual process of extracting information from observations, and of understanding patterns in a principled manner. This process and the deployment of data-centric technologies have recently brought unprecedented advances in many scientific fields, as well as increased global prosperity with the advent of knowledge-based economies and systems. At a high level, this revolution is driven by two thrusts: the modern technologies which allow for the collection of complex data sets, and the theories and algorithms we use to make sense of them. That said, and for all its benefits, extracting actionable knowledge from data is difficult. Observations gathered in uncontrolled environments are often high-dimensional, complex and noisy; and even when controlled experiments are used, the intricate systems that underlie them --- like those from meteorology, chemistry, medicine and biology --- can yield data sets with highly nontrivial underlying topology. This refers to properties such as the number of disconnected pieces (i.e., clusters), the existence of holes or the orientability of the data space. The research funded through this CAREER award will leverage ideas from algebraic topology to address data science questions like visualization and representation of complex data sets, as well as the challenges posed by nontrivial topology when designing learning systems for prediction and classification. This work will be integrated into the educational program of the PI through the creation of an online TDA (Topological Data Analysis) academy, with the dual purpose of lowering the barrier of entry into the field for data scientists and academics, as well as increasing the representation of underserved communities in the field of computational mathematics. The project provides research training opportunities for graduate students.

Understanding the set of maps between topological spaces has led to rich and sophisticated mathematics, for it subsumes algebraic invariants like homotopy groups and generalized (co)homology theories. And while several data science questions are discrete versions of mapping space problems --- including nonlinear dimensionality reduction and supervised learning --- the corresponding theoretical and algorithm treatment is currently lacking. This CAREER award will contribute towards remedying this situation. The research program articulated here seeks to launch a novel research program addressing the theory and algorithms of how the underlying topology of a data set can be leveraged for data modeling (e.g., in dimensionality reduction) as well as when learning maps between complex data spaces (e.g., in supervised learning). This work will yield methodologies for the computation of topology-aware and robust multiscale coordinatizations for data via classifying spaces, a computational theory of topological obstructions to the robust extension of maps between data sets, as well as the introduction of modern deep learning paradigms in order to learn maps between non-Euclidean data 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." "2405448","Applications of parametarized gauge theory","DMS","OFFICE OF MULTIDISCIPLINARY AC, TOPOLOGY","07/15/2024","07/15/2024","David Auckly","KS","Kansas State University","Standard Grant","Swatee Naik","06/30/2027","$293,046.00","","dav@math.ksu.edu","1601 VATTIER STREET","MANHATTAN","KS","665062504","7855326804","MPS","125300, 126700","9150","$0.00","The study of higher-dimenional spaces has had applications to many different areas, ranging from computer vision to data science. These spaces have many unique and beautiful patterns. Studying these patterns is worthwhile in its own right and may lead to unexpected important applications in the future. Four dimensions is the setting for Einstein?s theory of General Relativity where it is referred to as space-time. Four dimensional spaces have many interesting and unexpected properties. For example, one may find pairs of surfaces so that one surface may be deformed into another, but any such deformation will fail to be smooth in an essential way. Many of the differences between smooth and continuous objects related to four-dimensional spaces disappear after one of several possible stabilization operations is performed enough times. Detecting the required number of stabilizations is a difficult problem because many of the tools that may be used to detect differences between smooth objects fail to work after one stabilization. Using invariants for families of objects is one approach, but many of the key problems are still difficult. The approach this project takes is to consider several related questions where more structure is present. Sometimes the extra structure will make the problem more difficult, but sometimes the extra structure will make the problem easier. The hope is that resolving some of these related questions will provide insight into the more difficult, and more fundamental questions. This is where this project derives its intellectual merit. In addition to the pure research, the PI shares mathematics with many different communities. Notably, the PI is the director of the Navajo Nation Math Circles. Several mathematical activities presented in this community were inspired by more technical problems from the PIs research. This outreach program is the most notable broader impact of the project.

In more technical terms, the difficult problem is to find a pair of closed, simply connected, smooth 4 manifolds separated by more than one stabilization. The related approachable questions are analogues for embedded surfaces, diffeomorphisms, and families of such objects. The project will investigate a possible Arf-type invariant for pairs of surfaces, stabilization questions in the symplectic category as well as in families. It will also consider algebraic structures arising from these spaces. Some impacts arise because ideas developed and shared in this proposal may inspire work in adjacent fields. Other impacts arise due to the training and mentoring of future researchers and the mentoring of junior researchers that will take place in this research. The PI is an organizer for Gauge Theory Virtual and runs the MathCircles YouTube channel. The PI has close ties to the Navajo Nation and shares mathematics inspired by his research with this 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." @@ -30,7 +35,6 @@ "2350113","Conference: Topology Students Workshop 2024","DMS","TOPOLOGY","04/01/2024","02/22/2024","Dan Margalit","TN","Vanderbilt University","Standard Grant","Swatee Naik","03/31/2025","$34,972.00","Caitlin Leverson, Rebecca Winarski","dan.margalit@vanderbilt.edu","110 21ST AVE S","NASHVILLE","TN","372032416","6153222631","MPS","126700","7556","$0.00","This award provides support for the 7th biennial Topology Students Workshop (TSW) that will be held at Vanderbilt University during June 10-14, 2024. This is a five-day research and professional development activity for graduate students in the fields of geometric group theory, geometry, and topology, designed to expose graduate students to a wide range of current research, and to build their communication, networking, and problem-sharing skills. Approximately forty graduate students will participate, guided by ten mentors, who come from a wide range of career stages and research backgrounds within this field. The professional development and research sides of the workshop run in tandem, with mentors giving guidance in both areas. The workshop format devotes ample time for active networking and critiquing of research presentations.

The primary goals of TSW are to a) expose graduate students to a wide range of current research in topology, b) build their communication, networking, and problem-sharing skills, and c) give guidance on necessary but typically untaught aspects of the profession. The research portion covers a broad array of topics within geometry and topology including contact and symplectic topology, 3-manifolds, hyperbolic geometry, group actions, and complex dynamics. Professional development sessions include topics such as how best to benefit from conference participation and aim to build confidence and research potential among students. The workshop includes structured sessions on networking and etiquette, the job application process, communication skills, and a panel discussion on career paths that involves mathematicians from organizations such as NSA, Amazon, Google and private high schools. Mentors will also give research talks and suggest relevant problems to students who are embarking on a research career. The web site for the conference is http://www.danmargalit.net/tsw24.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405030","Collaborative Research: Algebraic K-theory and Equivariant Stable Homotopy Theory: Applications to Geometry and Arithmetic","DMS","TOPOLOGY","08/01/2024","05/14/2024","Michael Mandell","IN","Indiana University","Continuing Grant","Swatee Naik","07/31/2027","$69,737.00","","mmandell@iu.edu","107 S INDIANA AVE","BLOOMINGTON","IN","474057000","3172783473","MPS","126700","","$0.00","Algebraic topology began as the study of those algebraic invariants of geometric objects which are preserved under certain smooth deformations. Gradually, it was realized that the algebraic invariants called cohomology theories could themselves be represented by geometric objects, known as spectra. A central triumph of modern homotopy theory has been the construction of categories of ring spectra (representing objects for multiplicative cohomology theories) which are suitable for performing constructions directly analogous to those of classical algebra. This move has turned out to be incredibly fruitful, both by providing invariants which shed new light on old questions as well as by raising new questions which have unexpected connections to other areas of mathematics and physics. This research proposal studies such constructions in algebraic K-theory, the newly emerging field of Floer homotopy theory, and the foundations of equivariant stable homotopy theory. Broader impacts include workforce development in the form of graduate student advising, undergraduate and postdoc mentorship, high school mathematical science project mentorship, conference organization, and development of new education and training programs.

This proposal describes a broad research program to study a wide variety of problems in homotopy theory, geometry, and arithmetic. The PIs' prior work gives a complete description of the homotopy groups of algebraic K-theory of the sphere spectral at odd primes and a canonical identification of the fiber of the cyclotomic trace via a spectral lift of Tate-Poitou duality. In this proposal, the PIs describe a vast expansion of that argument to study the fiber of the cyclotomic trace on more general rings and schemes over algebraic p-integers in number fields and a related K-theory question more generally for other kinds of Artin duality. The prior work also leads to a new approach to the Kummer-Vandiver conjecture based on Bökstedt-Hsiang-Madsen's geometric Soule embedding that the PIs propose to study. The PIs' recent work with Yuan established a theory of topological cyclic homology (TC) relative to MU-algebras, where there are many interesting computations to explore. Prior work of PI Blumberg with Abouzaid building a Morava K-theory Floer homotopy type has opened new lines of research in Floer homotopy theory; this already has been used to resolve old conjectures in symplectic geometry. The PIs propose to extend this construction to its natural generality, building the homotopy type over MUP and KU and rigidifying the multiplication. They propose to obtain spectral models of deformed operations on quantum cohomology (i.e., quantum Steenrod operations). This work will have myriad applications in symplectic geometry and potentially have transformative impact on the Floer homotopy theory program. The PIs propose to resolve the longstanding confusion about the role of multiplicative norm maps in equivariant stable homotopy theory for positive dimensional compact Lie groups. This requires a new foundation for factorization homology and will lead to genuine equivariant factorization homology for positive dimensional compact Lie groups. In prior work, the PIs identified previously unknown multiplicative transfers on geometric fixed points of G-commutative ring spectra. The PIs propose to study how these fit into the foundations of G-symmetric monoidal categories; a first step is to establish new multiplicative splittings that have the feel of multiplicative versions of the tom Dieck splitting.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2414922","Stable Homotopy Theory in Algebra, Topology, and Geometry","DMS","TOPOLOGY","01/15/2024","01/23/2024","James Quigley","VA","University of Virginia Main Campus","Standard Grant","Christopher Stark","11/30/2025","$185,923.00","","mbp6pj@virginia.edu","1001 EMMET ST N","CHARLOTTESVILLE","VA","229034833","4349244270","MPS","126700","","$0.00","Stable homotopy theory was developed throughout the twentieth century to study high-dimensional topological spaces. Since spheres are the fundamental building blocks of topological spaces, the stable stems, which encode the possible relations between high-dimensional spheres up to continuous deformation, are a central object of study. Beyond topology, the stable stems have surprisingly broad applications throughout mathematics, ranging from geometric problems, such as classifying differentiable structures on spheres, to algebraic problems, such as classifying projective modules over rings. This project will explore further applications of stable homotopy theory in algebra, topology, and geometry. Broader impacts center on online community building. The PI will continue co-organizing the Electronic Computational Homotopy Theory Online Research Community, which aims to increase inclusion at the undergraduate, graduate, and senior levels by organizing undergraduate research opportunities, graduate courses, online seminars, mini-courses, and networking events. To address inequality at the K-12 level, the PI will develop and manage a program pairing undergraduates from his home institution with students from local after-school programs for online tutoring. This program would circumvent certain barriers to participation, such as lack of access to transportation and facilities, which are common in traditional outreach.

Specific research projects include the study of the stable stems and their applications in geometric topology, algebro-geometric analogues of the stable stems and their connections to number theory, and equivariant analogues of algebraic K-theory and their applications in algebra and geometry. More specifically, building on previous work, the PI will study the stable stems using topological modular forms and the Mahowald invariant, aiming to deduce the existence of exotic spheres in new dimensions. In a related direction, the PI will use the kq-resolution introduced in previous work to study the motivic stable stems, an algebro-geometric analogues of the stable stems. The main goal is to apply the kq-resolution to relate the motivic stable stems to arithmetic invariants like Hermitian K-theory. Real algebraic K-theory, which encodes classical invariants like algebraic K-theory, Hermitian K-theory, and L-theory, will also be studied using the trace methods developed in previous work. The overarching goal is extending results from algebraic K-theory to real algebraic K-theory, thereby obtaining results for Hermitian K-theory and L-theory that will have applications in algebra and 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." -"2341204","Conference: Midwest Topology Seminar","DMS","TOPOLOGY","02/01/2024","01/19/2024","Mark Behrens","IN","University of Notre Dame","Standard Grant","Eriko Hironaka","01/31/2025","$49,500.00","Daniel Isaksen, Vesna Stojanoska, Manuel Rivera, Carmen Rovi","mbehren1@nd.edu","836 GRACE HALL","NOTRE DAME","IN","465566031","5746317432","MPS","126700","7556","$0.00","This NSF award supports the Midwest Topology Seminar, from 2023 to 2026, a continuation of a previously supported regional conference series in algebraic topology that meets three times per year and rotates between universities in the Midwest and Great Lakes areas. The next two meetings are at Loyola University (March 2024) and Indiana University (Spring 2024). The Midwest Topology Seminar has been running continuously since the early 1970s, with at least one of the yearly meetings held in Chicago, the hub of the network, and is a long-standing, reliable, low-key, and low-cost way for participants to keep up with the field. The audiences are always large and diversified, drawing faculty and graduate students from a broad range of institutions. The Midwest Topology Seminar serves as a nexus for a vibrant community of research mathematicians, optimizing the distribution of new ideas through the field, especially among early career research mathematicians and mathematicians away from the traditional centers of research.

The Midwest is a traditional and continuing center of algebraic topology; hence there is a strong source of local speakers. Programs are augmented with featured speakers from around the country. Algebraic topology has always been broadly construed to include homotopy theory, algebraic K-theory, geometric group theory, and high dimensional manifolds; more recently the series has explored connections to algebraic geometry, representation theory, number theory, low dimensional manifolds, and mathematical physics. Financial support will go to graduate students and research mathematicians with limited funds from other sources. The conference web site is http://www.rrb.wayne.edu/MTS/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405370","Embedding Calculus and its Applications","DMS","TOPOLOGY, EPSCoR Co-Funding","07/15/2024","07/02/2024","Robin Koytcheff","LA","University of Louisiana at Lafayette","Standard Grant","Eriko Hironaka","06/30/2026","$150,000.00","","koytcheff@louisiana.edu","104 E UNIVERSITY AVE","LAFAYETTE","LA","705032014","3374825811","MPS","126700, 915000","9150","$0.00","This project concerns spaces of embeddings, generalizing the question of whether a circle embedded in three dimensional space can be untangled to the question of whether an n-parameter family of embeddings (possibly in high dimensions) can be deformed to a constant family. The PI will study far-reaching extensions of the linking number of a pair of curves in 3-space in novel ways. This project will improve our understanding of embedded objects and their relatives, both for their intrinsic mathematical interest and for their myriad applications in algebra, geometry, and physics. The PI will also work toward broadening participation in mathematics at the University of Louisiana at Lafayette and in the wider region through minority recruitment efforts, national and university-wide initiatives, and undergraduate research mentorship.

The main technical tool pervading this project is the functor calculus of Goodwillie and Weiss, especially the variant known as embedding calculus. The embedding calculus will often serve as an organizational principle, with configuration spaces playing a key role in concrete implementations of it. The PI will use this method to study the algebraic topology of spaces of embeddings and spaces of diffeomorphisms of manifolds of various dimensions, including their integer-valued and torsion invariants. Related directions to be explored include the rigid geometry of embeddings; expansions and finite-type invariants of groups; and computational and probabilistic approaches to various linking phenomena.

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348092","Conference: Algebraic Structures in Topology 2024","DMS","TOPOLOGY","03/01/2024","01/04/2024","Manuel Rivera","IN","Purdue University","Standard Grant","Swatee Naik","02/28/2025","$46,650.00","Jeremy Miller, Ralph Kaufmann, Mona Merling","river227@purdue.edu","2550 NORTHWESTERN AVE # 1100","WEST LAFAYETTE","IN","479061332","7654941055","MPS","126700","7556","$0.00","This award provides support for US based participants in the conference ""Algebraic structures in topology 2024? that will take place from June 5th to June 14th, 2024 in San Juan, Puerto Rico. Algebraic topology is a field of theoretical mathematics whose main goal is to study different notions of ?shape? that belong to the realm of ?continuous? mathematics, using tools from algebra that belong to the ?discrete? realm. Algebraic topology has been applied successfully to other fields of mathematics, and, more recently, to science including quantum physics, solid state physics, string theory, data science, and computer science. This conference will focus on recent developments in algebraic topology and its applications. The conference will feature a series of events accessible to audiences at different levels. These include: 1) a three-day school with mini-courses accessible to graduate students and mathematicians from fields outside algebraic topology, 2) a public event with talks and discussions accessible to a general audience, 3) a week-long research conference featuring invited speakers and contributed talks in algebraic topology. Furthermore, the conference aims to engage with groups that are historically underrepresented in academic research in mathematics, particularly with mathematicians of Hispanic and Latin American origin, in a deep and direct manner. Geographically, culturally, as well as politically, the strategically selected location, Puerto Rico, sits between the mathematical communities based in United States, Canada, Europe, and Latin America. Along with a strong engagement with the local community, the event will feature works by a significant number of Hispanic mathematicians.

The overarching theme of the conference is the use of algebra to give structure to geometric contexts. The mini-courses will be on the topics of algebraic K-theory, configuration spaces, and string topology and aim to bring participants to the state-of-the-art in these subjects. The research talks will highlight recent breakthroughs in different sub-fields of algebraic topology including stable and chromatic homotopy theory, K-theory, higher category theory, higher algebra, derived geometry, operads, homological stability, configuration spaces, string topology, and topological data analysis and will be given by leading experts in these fields. By bringing together a diverse cohort of mathematicians working on different sub-fields, the organizers aim to foster new ideas and perspectives. The public lectures will discuss research in theoretical mathematics, and its relevance to society, science, and technology, with examples coming from topology.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2428995","Conference: Betti Numbers in Commutative Algebra and Equivariant Homotopy Theory","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","08/01/2024","06/17/2024","Claudia Miller","NY","Syracuse University","Standard Grant","Tim Hodges","07/31/2025","$15,000.00","","clamille@syr.edu","900 S CROUSE AVE","SYRACUSE","NY","13244","3154432807","MPS","126400, 126700","7556","$0.00","This award provides travel funding for US-based participants in the week-long workshop ?Betti numbers in commutative algebra and equivariant homotopy theory? to be held September 23?27, 2024, at Bielefeld University, in Bielefeld, Germany. The workshop centers on a series of long-standing conjectures that appear in parallel in two major fields of mathematics. The goal of the workshop is to bring together researchers from these two fields to discuss recent advances on these conjectures. Another goal is to train more researchers to work on these important problems and help them build connections between the two fields. The overarching goal of this award would be to increase US participation in this highly active area of research, and to foster collaborations between US mathematicians and those from other countries. The funding is aimed especially at postdoctoral fellows and graduate students, as well as participants who do not have independent funding, to attend this workshop, and it will also be used to encourage participation by individuals from underrepresented groups in mathematics. A recent workshop held in Banff, Canada in 2022 initiated this goal, and funding for this event would cement the connections already made and build new ones for younger participants. The bridges we are building will not only connect researchers located in different countries but also between those working in different areas of mathematics.

Algebra and topology are thriving branches of mathematics that are well represented in most math departments. Commutative algebra, as the algebraic underpinnings of algebraic geometry, and algebraic topology, with its strong focus on homology and homotopy, have occasional significant overlap in both methods and aims. The goal is to create a strong working alliance between the groups working on these conjectures and related problems, and also to get younger researchers involved in these problems. In fact, total Betti numbers appear in related, decades-old rank conjectures in commutative algebra and equivariant topology. On the topological side, Halperin and Carlsson conjectured that the total Betti number of a compact space with a free torus action or p-torus action of rank r is bounded below by 2r, which has inspired much research on the topological side of spaces with a group action. On the algebraic side, Avramov conjectured a similar lower bound for the total Betti number of finite length modules over a local ring. Recent work of Walker and VandeBogert-Walker resolves this conjecture positively for rings of prime characteristic, whereas counterexamples to a stronger conjecture show the subtlety of the questions. The web site for the workshop is at https://www.math.uni-bielefeld.de/birep/meetings/betti2024/index.php and includes a full speaker list.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." @@ -50,20 +54,17 @@ "2407438","Problems in Non-Positive Curvature","DMS","TOPOLOGY","05/01/2024","05/01/2024","Jean-Francois Lafont","OH","Ohio State University","Standard Grant","Eriko Hironaka","04/30/2027","$332,834.00","","jlafont@math.ohio-state.edu","1960 KENNY RD","COLUMBUS","OH","432101016","6146888735","MPS","126700","","$0.00","Geometry is concerned with quantitative features of a space, while topology studies qualitative aspects of a space. As an example, a teacup and a donut are topologically the same (they both have a single hole), but geometrically different. Non-positive curvature is a geometric property of spaces, which roughly corresponds to the space being expansive at every point and in every direction. Spaces with this property are pervasive, both in mathematics and in nature. As a result, there are numerous different viewpoints and approaches to their study. This proposal is focused on a variety of problems that are loosely centered around non-positively curved spaces. The approaches are highly interdisciplinary, drawing on tools and techniques from various distinct areas of mathematics. This project also provides opportunities for graduate student and postdoc research and training.


The Principal Investigator (PI) will work on various projects in non-positive curvature that fall into four broad categories. (1) Projects on Coxeter groups: the PI will construct high-dimensional right-angled Coxeter groups that virtually algebraically fiber, will construct some new examples of negatively curved manifolds that fiber over the circle, and will construct new Davis manifolds that are CAT(0) but do not support Riemannian non-positive curvature smoothing. (2) Projects on simplicial volume: the PI will study which 4-dimensional Davis manifolds have positive simplicial volume, and will study how Anasov diffeomorphims constrain the simplicial volume. (3) Construtions of new aspherical manifolds: the PI will construct some new non-arithmetic hyperbolic manifolds, some new negatively curved Riemannian manifolds, and will study the commensurability problem for these manifolds. (4) Geodesic flows: the PI will study the decay of correlations for geodesic flows on locally CAT(-1) spaces, and will construct a version of the Sinai-Ruelle-Bowen measures for these flows.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2403798","Motivic to C2-Equivariant Homotopy and Beyond","DMS","TOPOLOGY, EPSCoR Co-Funding","08/15/2024","04/26/2024","Bertrand Guillou","KY","University of Kentucky Research Foundation","Standard Grant","Eriko Hironaka","07/31/2027","$245,299.00","","bertguillou@uky.edu","500 S LIMESTONE","LEXINGTON","KY","405260001","8592579420","MPS","126700, 915000","9150","$0.00","The problem of classifying mappings of a high-dimensional sphere onto a sphere of lower dimension is a central problem in algebraic topology and has repercussions in geometry and physics. The PI will focus on the context of mappings that preserve special symmetries of the spheres. The research will use recent theoretical developments to advance computational knowledge in this area. This research will be integrated with mentoring activities in the electronic Computational Homotopy Theory (eCHT) community and will be involved in recruiting for activities run by eCHT such as seminars, courses, and networking events for graduate students and postdocs. As an online community, the eCHT increases access to the research community, for example for people with geographical restrictions as well as for those with physical disabilities.

The PI and collaborators will leverage motivic/synthetic homotopy theory to perform computations of equivariant stable homotopy groups for the (cyclic) group of order 2, the Klein four group, and the quaternion group of order 8. The main tools to be used are the Bockstein, Adams, and slice spectral sequences. Various techniques will be employed to run these spectral sequences, including the use of Massey products. The PI and collaborators will also work to establish the height 1 Telescope Conjecture in the R-motivic and cyclic-2-equivariant settings, giving a description of certain periodic elements in the corresponding stable homotopy groups.

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

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2403817","Conference: 38th Summer Conference on Topology and Its Applications","DMS","TOPOLOGY, FOUNDATIONS","07/01/2024","04/23/2024","Will Brian","NC","University of North Carolina at Charlotte","Standard Grant","Qun Li","06/30/2025","$30,000.00","","wbrian.math@gmail.com","9201 UNIVERSITY CITY BLVD","CHARLOTTE","NC","282230001","7046871888","MPS","126700, 126800","7556","$0.00","This project supports the 38th annual Summer Topology Conference, hosted at the University of Coimbra in Coimbra, Portugal, July 8-12, 2024. This international conference encourages participation from a broad spectrum of mathematicians at different career levels and diverse backgrounds, and implements a recruitment strategy that starts with establishing a diverse cohort of session organizers. Elements of the conference provide pathways to include mathematicians into the community of topology research, such as dissemination of results through the conference affiliated journal Topology Proceedings. The funds from this grant will be used to support the participation of researchers based in the US, who wish to attend the conference but otherwise lack the funds to do so.

The conference will feature six special sessions: Set-theoretic Topology, Topological Methods in Algebra and Analysis, Topological Dynamics and Continuum Theory, Topology and Categories, Topology in Logic and Computer Science, and Topology and Order. There will be seven plenary lectures, as well as six semi-plenary lectures, one for each section. The extra plenary lecture will be delivered, per tradition, by this year's winner of the Mary Ellen Rudin Young Researcher Award. The primary goal of the conferences is to disseminate and discuss new discoveries in topology from the past few years, and to facilitate collaboration among those able to attend. Further information about the conference can be found at https://www.mat.uc.pt/~sumtopo/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2350370","Conference: CMND 2024 program: Field Theory and Topology","DMS","INFRASTRUCTURE PROGRAM, TOPOLOGY","05/01/2024","01/18/2024","Pavel Mnev","IN","University of Notre Dame","Standard Grant","Qun Li","04/30/2025","$39,360.00","Stephan Stolz, Christopher Schommer-Pries","Pavel.N.Mnev.1@nd.edu","836 GRACE HALL","NOTRE DAME","IN","465566031","5746317432","MPS","126000, 126700","7556","$0.00","The program ?Field theory and topology? to be held at the Center for Mathematics at Notre Dame (CMND), June 3?21, 2024 will continue the line of CMND summer programs and consists of a graduate/postdoctoral summer school, a conference, and an undergraduate summer school. The program will expose a new generation of undergraduates and early-career researchers to the new ideas, developments, and open problems in the exciting meeting place between topology and quantum field theory where many surprising advances were made recently.

There is a rich interplay between quantum field theory and topology. The program ?Field theory and Topology? will focus on recent extraordinary developments in this interplay -- new invariants of manifolds and knots coming from field-theoretic constructions; new languages and paradigms for field theory coming from interaction with topology: functorial field theory, cohomological (Batalin-Vilkovisky) approach, approach via derived geometry and via factorization algebras. Among subjects discussed at the program will also be supersymmetric and extended topological field theories, holomorphic twists. Webpage of the event: https://sites.nd.edu/2024cmndthematicprogram/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349810","Conference: Richmond Geometry Meeting: Geometric Topology and Moduli","DMS","ALGEBRA,NUMBER THEORY,AND COM, TOPOLOGY","05/01/2024","12/07/2023","Nicola Tarasca","VA","Virginia Commonwealth University","Standard Grant","Qun Li","10/31/2025","$26,430.00","Marco Aldi, Allison Moore","tarascan@vcu.edu","910 WEST FRANKLIN ST","RICHMOND","VA","232849005","8048286772","MPS","126400, 126700","7556","$0.00","This award supports the Richmond Geometry Meeting: Geometric Topology and Moduli scheduled for August 9-11, 2024, hosted at Virginia Commonwealth University in Richmond, VA. The conference is designed to unite experts in low-dimensional topology and algebraic geometry, spanning diverse career stages and affiliations. Beyond lectures delivered by internationally recognized experts, vertically integrated participation will be fostered by a poster session showcasing the contributions of early-career researchers and a Career and Mentorship Panel.

The conference will investigate the intersection of low-dimensional topology, algebraic geometry, and mathematical physics. The roots of this interdisciplinary exploration trace back to Witten's groundbreaking work in the late 1980s and the emergence of the Jones polynomial in Chern-Simons theory. Since then, a landscape of profound connections between knot theory, moduli spaces, and string theory has emerged, due to the collective efforts of generations of mathematicians and physicists. Noteworthy developments include the deep ties between Heegaard Floer homology and the Fukaya category of surfaces, the intricate interplay revealed by Khovanov homology, and the correspondence of Gromov-Witten and Donaldson-Thomas theories. The study of moduli spaces of curves, as exemplified in Heegaard Floer homology, has played a pivotal role in several developments. The preceding three editions of the Richmond Geometry Meeting, encompassing both virtual and in-person gatherings, have showcased a wave of collaborative advancements in knot theory, algebraic geometry, and string theory. Topics such as braid varieties, Khovanov homotopy, link lattice homology, and the GW/DT correspondence in families have been explored, unveiling a nexus of interdependent breakthroughs. This award supports the fourth edition of the Richmond Geometry Meeting, providing a vital platform for the dissemination of the latest findings in this dynamic realm of research. For more information, please visit the Richmond Geometry Meeting website: https://math.vcu.edu/rgm

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405405","Algebraic Structures in String Topology","DMS","TOPOLOGY","07/01/2024","03/22/2024","Manuel Rivera","IN","Purdue University","Standard Grant","Eriko Hironaka","06/30/2027","$288,912.00","","river227@purdue.edu","2550 NORTHWESTERN AVE # 1100","WEST LAFAYETTE","IN","479061332","7654941055","MPS","126700","","$0.00","The goal of this project is to understand the general structure of string interactions in a background space, its significance in geometry and mathematical physics, and to carry out explicit computations using algebraic models. Interactions of strings, paths, and loops are ubiquitous throughout mathematics and science. These range from observable phenomena in fluid dynamics (vortex rings in a fluid coming together to become a new ring or self-intersecting and breaking apart into multiple rings) to patterns arising in areas of theoretical physics such as string theory and quantum field theory. String topology proposes a mathematical model to study these interactions in terms of operations defined by intersecting, reconnecting, and cutting strings (closed curves) evolving in time in a manifold. Giving a rigorous and complete description of the structure of string topology, which is one of the aims of the proposed project, will also provide solid foundations for physical theories. Furthermore, the physicially inspired theory of string topology turns out to inform theoretical questions in mathematics: probing a space through strings and studying how all possible interactions are organized also reveals intricate aspects of the background geometry. Building upon previous work of the PI, the project proposes to algebraicize string topology through tractable models obtained by decomposing, or discretizing, the underlying space into cells and using techniques from algebraic topology and homological algebra, two well developed active fields of pure mathematics. These models will be applicable to study a wide range of string interaction phenomena appearing in both pure and applied mathematics as well as in theoretical physics. The proposed project includes a broad educational component focused on fostering mathematical activity and access at multiple levels. This involves graduate student training, organization of summer workshops and conferences that bring together researchers from a wide variety of fields, and the support of periodic seminars at the PI?s institution.

In more technical detail, this project aims to study chain-level string topology with a focus on operations that are sensitive to geometric structure beyond the homotopy type of the underlying manifold. In particular, the PI proposes to construct a homotopy coherent structure lifting the Goresky-Hingston loop coalgebra (and its S^1-symmetric Lie cobracket version) originally defined on the homology of the space of free loops on a manifold relative to the constant loops. The construction of such structure will use an appropriate refinement of Poincaré duality and intersection theory at the level of chains on a finely triangulated manifold together with the theory of algebraic models for loop spaces of non-simply connected manifolds developed in previous work of the PI using techniques from Hochschild homology theory and Koszul duality theory. These models will be transparent enough to reveal the precise geometric ingredients that are necessary to construct a coherent hierarchy of higher structures for string topology. This hierarchy of chain-level operations will provide a rich source of computable and potentially new manifold invariants. Connections with symplectic geometry, homological mirror symmetry, and the theory of quantization will be explored.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." +"2348686","Conference: UnKnot V","DMS","INFRASTRUCTURE PROGRAM, TOPOLOGY","06/01/2024","03/12/2024","Allison Henrich","WA","Seattle University","Standard Grant","Qun Li","11/30/2024","$40,000.00","Colin Adams, Elizabeth Denne","henricha@seattleu.edu","901 12TH AVE","SEATTLE","WA","981224411","2062966161","MPS","126000, 126700","7556","$0.00","The UnKnot V Conference will be held at Seattle University in Seattle, WA on July 13-14th, 2024. UnKnot V, like the four undergraduate knot theory conferences that preceded it, will be a gathering of students who are interested in knot theory research together with their faculty and graduate student mentors. Participants who are new to knot theory and interested to learn more are also welcome to join in this community-building event. Accessible talks at UnKnot V will be given by world-renowned knot theory experts as well as students who are just beginning their work in this field. UnKnot V will also feature a mini workshop on using machine learning in knot theory research and one on recreational topology with the aim to inspire fun math outreach projects.

Knot theory is an area of research which uses tools from and gives insight into many areas of mathematics, including topology, geometry, algebra, and combinatorics. There are important applications in knot theory to DNA knotting, synthetic chemistry, protein folding, and quantum computing as well as in anthropology, art, and materials science. Knot theory also lends itself to research by undergraduates since there are open problems that can be easily stated and explained but lead to mathematics with great depth. The focus of UnKnot V will be on research that has been done by undergraduates and on open problems amenable to research by students. Since experts will be brought together with the students and faculty who would like to do research in this field, this unique conference structure will allow for vertical integration from undergraduates and graduate students to faculty who are interested in mentoring students in knot theory research and experts in the field. Many opportunities for research projects will be presented. The conference webpage is: https://sites.google.com/view/unknot-v-conference/home.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2348830","Conference: 57th Spring Topology and Dynamical Systems Conference","DMS","TOPOLOGY, FOUNDATIONS","02/15/2024","02/13/2024","Will Brian","NC","University of North Carolina at Charlotte","Standard Grant","Eriko Hironaka","01/31/2025","$33,000.00","Hector Barriga-Acosta","wbrian.math@gmail.com","9201 UNIVERSITY CITY BLVD","CHARLOTTE","NC","282230001","7046871888","MPS","126700, 126800","7556","$0.00","This proposal supports the 57th annual Spring Topology and Dynamical Systems conference (STDC), hosted this year at the University of North Carolina at Charlotte. The conference encourages participation from a broad spectrum of mathematicians at different career levels and diverse backgrounds and implements a recruitment strategy that starts with establishing a diverse cohort of session organizers. Elements of the conference include providing pathways to including mathematicians into the community, such as dissemination of results through the conference affiliated journal Topology Proceedings. Conference funds will be used to support graduate students and early career participants, as well as established mathematicians without other sources of travel support and invited speakers.

The 57th STDC will be the latest in an annual series that began in 1967 and will continue its tradition of bringing together researcher from the around the world and from a range of currently active areas of topology. Over the years, the conference has structured itself around a core of special sessions representing strands of topology-related fields of interest. The 57th STDC will feature sessions focused on Continuum Theory, Dynamical Systems, Geometric Group Theory, Geometric Topology, and Set-Theoretic Topology. More information about the conference is available at: https://pages.charlotte.edu/stdc2024/.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2340239","CAREER: Elliptic cohomology and quantum field theory","DMS","TOPOLOGY","06/15/2024","01/10/2024","Daniel Berwick Evans","IL","University of Illinois at Urbana-Champaign","Continuing Grant","Eriko Hironaka","05/31/2029","$73,192.00","","danbe@illinois.edu","506 S WRIGHT ST","URBANA","IL","618013620","2173332187","MPS","126700","1045","$0.00","The research of this award lies at the interface between theoretical physics and geometry. An unsolved conjecture posits a deep connection between the geometry of supersymmetric quantum field theories and certain structures in algebraic topology. Resolving this conjecture would provide new insight into the mathematical foundations of quantum field theory, while also providing several long-anticipated applications of algebraic topology in physics. The projects the PI will work on leverage higher categorical symmetries to gain new insights into this 30-year-old conjecture. The award supports graduate students working with the PI whose research will contribute to this area. The PI will also continue his involvement in mathematics education for incarcerated people through the Education Justice Project in Illinois.

The proposed research is centered on an equivariant refinement of Stolz and Teichner?s conjectured geometric model for elliptic cohomology from 2-dimensional supersymmetric field theories. The overarching goal is to link structures in Lurie?s 2-equivariant elliptic cohomology with the geometry of supersymmetric gauge theories. Some of the projects are natural extensions of prior work at heights zero and one, focusing on height 2 generalizations of specific quantum field theories that are expected to construct elliptic Thom classes. Other projects will initiate the study of 2-equivariant geometry, interfacing with topics in string geometry, loop group representation theory, and elliptic power operations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2348686","Conference: UnKnot V","DMS","INFRASTRUCTURE PROGRAM, TOPOLOGY","06/01/2024","03/12/2024","Allison Henrich","WA","Seattle University","Standard Grant","Qun Li","11/30/2024","$40,000.00","Colin Adams, Elizabeth Denne","henricha@seattleu.edu","901 12TH AVE","SEATTLE","WA","981224411","2062966161","MPS","126000, 126700","7556","$0.00","The UnKnot V Conference will be held at Seattle University in Seattle, WA on July 13-14th, 2024. UnKnot V, like the four undergraduate knot theory conferences that preceded it, will be a gathering of students who are interested in knot theory research together with their faculty and graduate student mentors. Participants who are new to knot theory and interested to learn more are also welcome to join in this community-building event. Accessible talks at UnKnot V will be given by world-renowned knot theory experts as well as students who are just beginning their work in this field. UnKnot V will also feature a mini workshop on using machine learning in knot theory research and one on recreational topology with the aim to inspire fun math outreach projects.

Knot theory is an area of research which uses tools from and gives insight into many areas of mathematics, including topology, geometry, algebra, and combinatorics. There are important applications in knot theory to DNA knotting, synthetic chemistry, protein folding, and quantum computing as well as in anthropology, art, and materials science. Knot theory also lends itself to research by undergraduates since there are open problems that can be easily stated and explained but lead to mathematics with great depth. The focus of UnKnot V will be on research that has been done by undergraduates and on open problems amenable to research by students. Since experts will be brought together with the students and faculty who would like to do research in this field, this unique conference structure will allow for vertical integration from undergraduates and graduate students to faculty who are interested in mentoring students in knot theory research and experts in the field. Many opportunities for research projects will be presented. The conference webpage is: https://sites.google.com/view/unknot-v-conference/home.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405191","A1-Homotopy Theory and Applications to Enumerative Geometry and Number Theory","DMS","TOPOLOGY","06/01/2024","02/26/2024","Kirsten Wickelgren","NC","Duke University","Standard Grant","Eriko Hironaka","05/31/2027","$405,500.00","","kirsten.wickelgren@duke.edu","2200 W MAIN ST","DURHAM","NC","277054640","9196843030","MPS","126700","","$0.00","This award supports a research program involving an enriched form of counting to study the solutions of equations and the spaces they form. It matters if the solution to a set of equations can be expressed using the usual counting numbers, or if real numbers are required, or if one must use imaginary numbers. The enriched count detects such differences. In some cases, it is closely connected to the number of holes of dimension d in the shape of a space of real solutions to the equations. This project exploits the power of the enriched count, exposing potential applications in number theory and algebraic geometry. The award will also support a pipeline for a strong and diverse mathematical workforce. This will involve a continuing program of week-long summer math jobs for gifted high school students from diverse backgrounds. During this program, the PI will facilitate collaborative projects with high school student and teachers, providing background material as necessary. Graduates from the summer program will be encouraged to continue on to a Research Experience for Undergraduates that will provide further mathematical training and research mentorship.

The proposed research studies number-theoretic and algebro-geometric questions using cohomology theories and homotopical methods in the framework of Morel and Voevodsky's A1-homotopy theory. The project uses stable A1-homotopy theory to produce results in enumerative geometry over non-algebraically closed fields and rings of integers. New Gromov--Witten invariants defined over general fields have the potential to satisfy wall-crossing formulas, surgery formulas, and WDVV equations. For this, the project studies notions of spin over general fields. The Weil conjectures connect the number of solutions to equations over finite fields to the topology of their complex points: The zeta function of a variety over a finite field is simultaneously a generating function for the number of solutions to its defining equations and a product of characteristic polynomials of endomorphisms of cohomology groups. The ranks of these cohomology groups are the Betti numbers of the associated complex manifold. The logarithmic derivative of the zeta function is enriched to a power series with coefficients in the Grothendieck--Witt group, producing a connection with the associated real manifold. This project aims to increase our control over this logarithmic derivative of the zeta function and its applications.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2339110","CAREER: Rigidity in Mapping class groups and homeomorphism groups","DMS","TOPOLOGY","08/01/2024","01/10/2024","Lei Chen","MD","University of Maryland, College Park","Continuing Grant","Qun Li","07/31/2029","$95,422.00","","chenlei1991919@gmail.com","3112 LEE BUILDING","COLLEGE PARK","MD","207425100","3014056269","MPS","126700","1045","$0.00","In geometry and topology, one of the most fundamental objects is to study various geometric groups and their features. This project will investigate the rigidity problems concerning mapping class groups and homeomorphism groups of manifolds. The PI will use methods from dynamical systems, geometric group theory, low dimensional topology, and differential geometry. The educational activities include high school outreach, undergraduates research through REU projects, mentoring graduate students in the home institution, and workshops organizations.

Symmetry is a pervasive concept in mathematics. In the study of differential topology, the full symmetry group is the diffeomorphism group of a manifold. There are two sides of a diffeomorphism group: one is the mapping class group, the group of connected components of a diffeomorphism group; the other is the identity component of a diffeomorphism group, which is a connected topological group. The PI will study these groups using both geometric group theory through the study of how those groups act on certain complexes and dynamical tools through the study of how those groups act on other manifolds.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2340341","CAREER: Large scale geometry and negative curvature","DMS","TOPOLOGY","09/01/2024","01/25/2024","Carolyn Abbott","MA","Brandeis University","Continuing Grant","Eriko Hironaka","08/31/2029","$113,427.00","","carolynabbott@brandeis.edu","415 SOUTH ST","WALTHAM","MA","024532728","7817362121","MPS","126700","1045","$0.00","The symmetries of a space and its relation to the underlying geometric structure of the space has led researchers to deep insights into the connections between algebraic and geometric structures. This project focuses on hyperbolic spaces and the coarse geometry their structure induces on their associated symmetry groups. The project activity also includes initiatives in teaching and mentoring mathematics students at all levels, with a focus on targeting students from under-represented populations both at the department and in the region.

The funded research has three main goals: to generalize notions of coarse negative curvature, particularly acylindrical hyperbolicity, to a broad class of topological groups; to establish a strong stability result for quotients of hierarchically hyperbolic groups, a class of groups which can be completely described by their actions on hyperbolic metric spaces; and to extend combinatorial methods from cubical groups to the larger class of CAT(0) groups, with a focus on aspects of negative curvature and boundaries. Parts of this research program will be incorporated into student projects as a way to expand access to undergraduate research at the PI?s institution.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349401","Conference: Combinatorial and Analytical methods in low-dimensional topology","DMS","TOPOLOGY","04/01/2024","01/10/2024","Francesco Lin","NY","Columbia University","Standard Grant","Eriko Hironaka","03/31/2026","$26,000.00","","fl2550@columbia.edu","615 W 131ST ST","NEW YORK","NY","100277922","2128546851","MPS","126700","7556","$0.00","This NSF award will support the participation of U.S. based participants to the conference ?Combinatorial and Gauge theoretical methods in low-dimensional topology and geometry?, to be held at Centro di Ricerca Matematica Ennio De Giorgi in Pisa (Italy) in June 3-7, 2024. The conference will bring together experts in combinatorial and analytical techniques in low-dimensional topology with the aim of exploring new interactions between the two sets of tools. In particular, the grant will fund the participation of young researchers with the concrete goal of fostering new international collaborations.

The past few decades have seen a tremendous advancement in our understanding of low-dimensional topology, and several of the most original results have come to light when the tools from analysis and combinatorics are used in combination. The conference will explore new developments in topics at this interface such as: knot theory, braid groups, and mapping class groups; constructions and obstructions in 4-dimensional topology; classification questions in contact and symplectic geometry; singularity theory and its relation with Floer theory. More details can be found on the conference website: http://www.crm.sns.it/event/519/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"2427220","Computations in Classical and Motivic Stable Homotopy Theory","DMS","TOPOLOGY","04/01/2024","04/09/2024","Eva Belmont","OH","Case Western Reserve University","Standard Grant","Swatee Naik","06/30/2025","$106,619.00","","eva.belmont@case.edu","10900 EUCLID AVE","CLEVELAND","OH","441061712","2163684510","MPS","126700","","$0.00","Algebraic topology is a field of mathematics that involves using algebra and category theory to study properties of geometric objects that do not change when those objects are deformed. A central challenge is to classify all maps from spheres to other spheres, where two maps are considered equivalent if one can be deformed to the other. The equivalence classes of these maps are called the homotopy groups of spheres, and collectively they form one of the deepest and most central objects in the field. Historically, much important theory has arisen out of attempts to compute more homotopy groups of spheres and understand patterns within them. This project involves furthering knowledge of the homotopy groups of spheres, using old and new techniques as well as computer calculations. The project also involves studying an analogue of these groups in algebraic geometry; this falls under a relatively new and actively developed area called motivic homotopy theory, which applies techniques in algebraic topology to study algebraic geometry. The broader impacts of this project center around supporting the local mathematics community through mentoring and promoting diversity. The principal investigator will help build the nascent homotopy theory community at the university and promote women and minorities in the subject through seminar organization and mentoring.

One of the main planned projects is a large-scale effort to compute the homotopy groups of spheres at the prime 3 in a range, using old and new techniques such as the Adams-Novikov spectral sequence as well as infinite descent machinery. This work will be aided by computer calculations, which short-circuits some of the technical difficulties encountered in previous attempts. Another main group of projects concerns computing the analogue of the stable homotopy groups of spheres in the world of R-motivic homotopy theory. This represents a continuation of prior work of the PI and collaborator; the plan is to supplement the techniques used in that work with computer calculations and a new tool, the slice spectral sequence. A third project concerns theory and spectral sequence computations aimed at computing the cohomology of profinite groups such as special linear groups and Morava stabilizer groups.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2403833","Conference: Geometric and Asymptotic Group Theory with Applications 2024","DMS","TOPOLOGY","01/01/2024","12/18/2023","Jingyin Huang","OH","Ohio State University","Standard Grant","Swatee Naik","12/31/2024","$22,100.00","","huang.929@osu.edu","1960 KENNY RD","COLUMBUS","OH","432101016","6146888735","MPS","126700","7556","$0.00","The conference ?Geometric and Asymptotic Group Theory with Applications? will be held in Luminy, France February 5 - 9, 2024. This award provides partial travel support for a group of early career US based mathematicians to attend this conference. The conference has an interdisciplinarity nature, focusing on topics in the intersection of mathematics and computer science. A variety of leading experts working in the relevant fields will present their work. Early career US based participants will also be given the opportunity to give talks and thereby enhance their international profile. The exposure to recent developments in the field and the opportunities to communicate with their colleagues from all over the world is expected to initiate new research collaborations. Conference organizers will devote special efforts to recruit and encourage members of under-represented groups in mathematics.

The study of infinite groups is a very active area in modern mathematics. A major trend in this area is geometric group theory, which aims at understanding the asymptotic geometry of finitely generated groups. On the other hand, this seemingly geometric approach to infinite groups also has deep connections to the more classical theme of decidability, logic, and algorithmic aspects of group theory, which lie in the intersection of computer science and mathematics. This conference will bring together prominent researchers interested in group theory, but from different sub-fields and viewpoints, some on the geometric side, while others on the algorithmic/computation side, to present their work. The speakers are carefully chosen in order to emphasize connections between different aspects, and to stimulate further collaboration. A wide range of infinite groups of great importance will be discussed during the conference, including cubical groups, hyperbolic groups, automaton groups, automatic groups, Artin groups, Coxeter groups, self-similar groups, non-positively curved groups etc. More information is available on the webpage of the conference at https://conferences.cirm-math.fr/3149.html.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2349755","Conference: Mid-Atlantic Topology Conference 2024","DMS","TOPOLOGY","03/01/2024","02/22/2024","Benjamin Knudsen","MA","Northeastern University","Standard Grant","Swatee Naik","02/28/2025","$30,000.00","Jose Perea, Iva Halacheva, Thomas Brazelton","b.knudsen@northeastern.edu","360 HUNTINGTON AVE","BOSTON","MA","021155005","6173733004","MPS","126700","7556","$0.00","This National Science Foundation award provides funding for participants of the Mid-Atlantic Topology Conference, which will take place March 23 and 24, 2024 at Northeastern University in Boston. The conference will focus on a broad overview of trends in topology currently at the forefront of research, including geometric group theory, geometric and topological data analysis, applied and computational topology, higher category theory, and motivic homotopy theory. This conference will further advance the growing diversity within algebraic topology, as well as the strength and coherence of the East Coast topology community. It is the latest iteration in a series of recurring conferences aimed at uniting the increasingly active topology groups in this geographical area.

The conference will feature nine 45-minute talks spread over two days. Speakers have been chosen with particular emphasis on gender representation. They are predominantly early career researchers and hail from public and private institutions alike. Advertising and funding will be targeted to prioritize inclusion of participants from underrepresented populations, continuing a strategy proven to be successful in the last iteration of the conference. The conference will provide graduate students and postdoctoral researchers with invaluable networking and community building opportunities and will strengthen the regional fabric of the field of topology. Further
information is available at https://sites.google.com/northeastern.edu/matc2024/home.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2405684","Conference: 2024 Redbud Topology Conference","DMS","TOPOLOGY","03/01/2024","02/26/2024","Henry Segerman","OK","Oklahoma State University","Standard Grant","Swatee Naik","02/28/2025","$28,869.00","Jonathan Johnson, Neil Hoffman","henry@segerman.org","401 WHITEHURST HALL","STILLWATER","OK","740781031","4057449995","MPS","126700","7556, 9150","$0.00","This award provides funding for the 2024 Spring and Fall Redbud Geometry/Topology Conferences, the first of which is to be held April 12-14, 2024, at Oklahoma State University. These conferences are part of an ongoing series of conferences held at universities in Arkansas and Oklahoma, intended to increase interaction and collaboration among early career and established mathematicians in the area. The Spring meeting will feature talks by prominent speakers from across North America, as well as a graduate student workshop. The Fall meeting will take place at the University of Oklahoma, and it will predominantly consist of talks by early-career mathematicians from the EPSCoR regions of Arkansas, Oklahoma, and surrounding states.

Many interesting results have linked low-dimensional topology and group orderability. These results have provided evidence for a prominent conjecture addressing which three-manifold groups are left-orderable, and have made progress towards a classification of bi-orderable three-manifold groups. The 2024 Spring Redbud Geometry/Topology Conference will bring together leading researchers to discuss these developments. The invited speakers are: Idrissa Ba (University of Manitoba), Adam Clay (University of Manitoba), Nathan Dunfield (University of Illinois Urbana-Champaign), Cameron Gordon (University of Texas at Austin), Ying Hu (University of Nebraska, Omaha), Tao Li (Boston College), Rachel Roberts (Washington University in St. Louis), Dale Rolfsen (University of British Columbia), and Hannah Turner (Georgia Institute of Technology). The conference begins with a workshop designed to enhance the experience of graduate students and junior researchers. The workshop will feature expository talks by Clay, Gordon, and Rolfsen. More information is available at the conference website: https://math.okstate.edu/conferences/redbud/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." "2350309","Conference: St. Louis Topology Conference: Flows and Foliations in 3-Manifolds","DMS","TOPOLOGY","04/01/2024","12/18/2023","Michael Landry","MO","Saint Louis University","Standard Grant","Swatee Naik","03/31/2025","$34,920.00","Rachel Roberts, Steven Frankel","michael.landry@slu.edu","221 N GRAND BLVD","SAINT LOUIS","MO","631032006","3149773925","MPS","126700","7556","$0.00","This award provides participant support for the St. Louis Topology Conference taking place May 17-19, 2024 in St. Louis, Missouri, USA. The theme of the conference is Flows and Foliations in 3-manifolds. The mathematical concept of a dynamical system allows for any continuously time-varying physical system to be considered within a uniform framework, as a ?state space? that organizes all possible instantaneous configurations, together with a ?flow? that describes the evolution of states with time. The conference is focused on the way that the geometry and topology of a space interacts with the kinds of dynamical systems that it supports, with an eye towards applications in dynamics, geometry, and topology. The organizers are committed to broad recruitment across a diverse set of students and postdoctoral researchers. In addition to hour-long lectures by established researchers, there will be lightning talks as well as a panel discussion on issues faced by early career mathematicians.

Flows and foliations in three dimensional manifolds can be fruitfully viewed through many lenses, as they stand at the intersection of dynamics, topology, and geometry. Interest in this general area has accelerated since Agol's resolution of the Virtual Fibering Conjecture, with researchers using a variety of tools and ideas such as (pseudo-) Anosov and partially hyperbolic flows, sutured manifold hierarchies, geometric group theory, contact geometry, Floer theory, veering triangulations, and the so-called big mapping class group to study a variety of questions. These include among others the L-space conjecture, the Cannon Conjecture, the Pseudo-Anosov Finiteness Conjecture, and the classification of infinite-type mapping classes. Recent conferences have tended to focus on small subsets of these topics and techniques, and there is a need for an event at which researchers with expertise in these different topics can meet and share their knowledge. Talks will take place at Washington University. The conference website is https://sites.google.com/view/stltc/home.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria." -"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." "2350374","Collaborative Research: Conference: Workshops in Geometric Topology","DMS","TOPOLOGY","05/01/2024","01/23/2024","Jack Calcut","OH","Oberlin College","Standard Grant","Swatee Naik","04/30/2027","$25,350.00","","jcalcut@oberlin.edu","173 W LORAIN ST","OBERLIN","OH","440741057","4407758461","MPS","126700","7556","$0.00","This award provides support for three meetings of a well-established series of summer Workshops in Geometric Topology, with the first to be held at Calvin University in Grand Rapids, MI, June 13-15, 2024. The award will also fund workshops at Oberlin College in 2025 and University of Wisconsin-Milwaukee in 2026. These workshops provide an annual opportunity for active researchers and graduate students in the mathematical field of geometric topology to interact in a setting that provides multiple tangible benefits, including:
1) attending the lectures of a principal speaker to receive an in-depth introduction to important current streams of research being performed by nationally-recognized experts,
2) learning about a breadth of other research activities by attending shorter talks given by the other workshop participants,
3) the opportunity to share their own work by giving talks in a congenial environment, and
4) important time for informal discussion and interaction among participants and with the principal speaker.
These workshops regularly feature participation and talks by members of underrepresented groups in mathematics, and, to further broaden the impact of the workshops, the talks of the principal speaker will be recorded and posted to the internet. The workshops also provide significant benefits to graduate students by providing a serious but informal research atmosphere in which they can meet and learn from others in the field. NSF funding will be used to cover the attendance costs of workshop participants.

More specifically, the workshops provide opportunities for geometric topologists to interact and share ideas, leading to research collaborations. Furthermore, the proposed workshops will continue the tradition of inviting each year a renowned principal speaker to provide a series of three lectures on a topic of his or her choice for the purpose of expanding the interests of the participants by having a nationally-recognized expert discuss an important area of current interest. The 2024 workshop will feature Professor Maggie Miller of the University of Texas -- Austin. The web site for this workshop will be https://sites.google.com/view/workshop2024/home.

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