Project Grant 2404896
- This three-year $350,000 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program will support research at the University of Maryland, College Park on moduli spaces of Higgs bundles, gauge theory, and related topics in complex geometry. The principal investigator will further studies on moduli spaces of Higgs bundles on Riemann surfaces, including work on parabolic lambda-connections, construction of a universal moduli space, and the asymptotic and...
- This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research in two main areas: 1) the "Ghost Algebra for Correlation Functions of Anosov Representations" and 2) the "Weil Petersson Gradient Flow for Renormalized Volume". The $282,000 award, with a period of performance from August 15, 2024 to July 31, 2027, will fund the Principal Investigator's (PI) work to study the symplectic structure...
- This National Science Foundation Project Grant award of $315,130 provides funding from September 1, 2022 through August 31, 2024 to support research on topological symmetries of non-compact Riemann surfaces. The award is made under the Mathematical and Physical Sciences program (CFDA 47.049) to the Research Foundation of the City University of New York on behalf of Queens College. The principal investigator will conduct research focusing on understanding the algebraic structure of mapping...
- This three-year Project Grant from the National Science Foundation's Mathematical and Physical Sciences program ($160,000) will support research at Michigan State University exploring the connections between cluster algebras, quantum groups, and decorated character varieties. The principal investigator will investigate the quantum geometry of moduli spaces within the framework of cluster algebras, examining relationships between decorated character varieties, quantum groups, and Legendrian...
- This National Science Foundation Project Grant of $240,000 will support research using sheaf-theoretic methods in modular representation theory from September 1, 2022 to August 31, 2025. Under the Mathematical and Physical Sciences program (CFDA 47.049), the principal investigator at Louisiana State University will conduct research on three topics: the topology of global Schubert varieties, Kazhdan-Lusztig cells and tilting modules, and siltting complexes of coherent sheaves. This work aims to...
- The National Science Foundation (NSF) Division of Mathematical Sciences awarded a 3-year, $250,000 Project Grant to the University of Wisconsin - Madison under the Mathematical and Physical Sciences program (CFDA 47.049) to investigate moduli spaces of surfaces with additional geometric structure. The grant will fund research to solve long-standing conjectures about the geometry and topology of these moduli spaces, which are mathematical spaces that parameterize the shapes an object can take....
- This $249,410 National Science Foundation project grant supports research at Texas A&M University exploring the relationship between hyperbolic geometry and quantum invariants. Specifically, the grantee will study the asymptotics of quantum invariants and their connection to the hyperbolic volume of 3-dimensional manifolds and mapping tori of self-homeomorphisms of surfaces. The grantee will pursue three related research themes: developing an explicit formula for adjoint twisted Reidemeister...
- This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $300,000 in funding to the University of California, Los Angeles (UCLA) from July 1, 2025 to June 30, 2028. The award supports research on higher-dimensional contact topology and its relationship to quantum physics and quantum invariants of knots and links. Key focus areas include studying the mathematical structures underlying the relationship between Hecke...
- This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $100,000 in funding to Utah State University (USU) from August 1, 2025 to July 31, 2027. The project aims to advance research in Lie theory, a framework for understanding symmetry in algebra and geometry, with three key objectives: Developing a theory of universal abelianized centralizers for sheets in semisimple Lie algebras, which may yield new instances of...
- This National Science Foundation (NSF) Project Grant award for $155,000 supports research and education activities at Utah State University in the field of representation theory and its applications to theoretical physics. The project, which runs from September 1, 2023 to August 31, 2026, involves three related research initiatives: Developing a theory of real equivariant matrix factorizations and applying it to study Landau-Ginzburg orientifolds. Extending prior work on the representation...
GEOMETRY OF MODULI SPACES AND METAPLECTIC REPRESENTATIONS -CONFORMAL FIELD THEORIES, ROOTED IN THEORETICAL PHYSICS, OFFER A POWERFUL FRAMEWORK FOR GEOMETERS TO STUDY ALGEBRAIC CURVES. WHILE TRADITIONALLY FOCUSED ON CURVES, RECENT ADVANCEMENTS IN THE GEOMETRIC MANIFESTATIONS OF INFINITE-DIMENSIONAL ALGEBRAS SUGGEST THE EMERGENCE OF A RICH THEORY APPLICABLE TO HIGHER-DIMENSIONAL VARIETIES AS WELL. MOTIVATED BY PROMISING PRELIMINARY FINDINGS, THE PI WILL LEAD AN EXPLORATION OF CONFORMAL FIELD THEORIES EXTENDING BEYOND CURVES, PROBING FUNDAMENTAL QUESTIONS CONCERNING THE GEOMETRY OF HIGHER-DIMENSIONAL VARIETIES. SIMILARLY, THE PI WILL INVESTIGATE INVARIANTS FOR KNOTS AND 3-MANIFOLDS. THIS PROJECT WILL FUEL THE INTEGRATION OF IDEAS FROM SEVERAL FIELDS OF MATHEMATICS, SUCH AS REPRESENTATION THEORY, ALGEBRAIC GEOMETRY, AND QUANTUM TOPOLOGY. IT WILL ALSO FEATURE EXPERIENTIAL LEARNING INITIATIVES TAILORED FOR MIDDLE SCHOOL STUDENTS, ALONGSIDE RESEARCH TRAINING OPPORTUNITIES DESIGNED FOR UNDERGRADUATE AND GRADUATE STUDENTS. FURTHERMORE, THE PROJECT AIMS TO FOSTER INTERDISCIPLINARY COLLABORATIONS AND ENHANCE MATHEMATICAL LITERACY WITHIN THE GENERAL PUBLIC THROUGH A SERIES OF PUBLIC LECTURES AND EVENTS. MORE SPECIFICALLY, THE PI WILL BUILD UPON RECENT WORK ON COINVARIANTS OF VERTEX ALGEBRAS TO EXPLORE GEOMETRIC REALIZATIONS OF METAPLECTIC MODULES ON ABELIAN VARIETIES AND THEIR MODULI SPACES. THESE INVESTIGATIONS WILL OFFER A NOVEL PERSPECTIVE ON THE THEORY OF THETA FUNCTIONS AND VECTOR BUNDLES EQUIPPED WITH A PROJECTIVELY FLAT CONNECTION ON FAMILIES OF ABELIAN VARIETIES. FURTHERMORE, THE PI WILL INVESTIGATE THE FACTORIZATION PROPERTIES OF SPACES OF COINVARIANTS ON DECOMPOSABLE ABELIAN VARIETIES, FOLLOWED BY AN ASSESSMENT OF THE PERSISTENCE OF THESE PROPERTIES AT BOUNDARY POINTS ACROSS VARIOUS COMPACTIFICATIONS. FINALLY, THE PI WILL EXPLORE VARIOUS REFINEMENTS OF THE THEORY OF HOMOLOGICAL BLOCKS FOR KNOTS AND 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.- SUBAWARDS ARE NOT PLANNED FOR THIS AWARD.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $192.2k | 7/21/25 | ||
| Not listed | $100.0k | 5/30/24 |