Project Grant 2505908
- This National Science Foundation (NSF) Project Grant, awarded under the Mathematical and Physical Sciences program (CFDA 47.049), provides $172,247 to support collaborative research on small quantum groups, their categorifications, and topological applications. The research aims to bridge the gap between 3D topological quantum field theories and our 4D universe, with a focus on developing homological invariants of 3D and 4D manifolds. The project will involve students and postdocs,...
- This Project Grant award, titled "UNIFYING TQFTS FOR GL(1,1) AND THE ALEXANDER POLYNOMIAL", is funded by the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program. The $120,250 award will support research into the mathematical and quantum mechanical phenomena underlying topological insulators and topological quantum computing. Specifically, the project will study the Frohman-Nicas Topological Quantum Field Theory (TQFT) for the Alexander...
- 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 $299,996 Project Grant award from the National Science Foundation's (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental mathematical research by a team at Utah State University. The project aims to develop new algebraic and geometric tools to formalize and advance the mathematical theory underlying quantum physics, particularly in low-dimensional topology and the theory of quantum invariants. The key products and...
- This Project Grant award, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), supports fundamental research into the topology and dynamics of four-dimensional manifolds with symplectic structures. The $156,571 award, spanning from September 1, 2024 to August 31, 2026, will enable the principal investigator to employ advanced mathematical tools, such as surgery on Lefschetz fibrations, Gromov-Witten theory, and family...
- 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 from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) provides $452,656 to California State University Fresno Foundation to support research in low-dimensional topology from September 1, 2022 to August 31, 2025. The funding will advance understanding of link homology theories and other quantum invariants through construction and study of new Khovanov-type homology theories for classical and singular knots. It will also investigate...
- This federal Project Grant award in the amount of $177,469.00 was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences Grant Program (CFDA #47.049). The award will support research into the geometry of moduli spaces from low-dimensional topology and applications, with a focus on three main directions: studying higher algebraic structures in instanton Floer homology, analyzing the properties of generalized Seiberg-Witten equations, and exploring the...
- The National Science Foundation awarded a $199,581 Project Grant to Texas A&M University under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The grant supports research focused on using curvature-like inequalities to study the distortion of geometric structures when mapped into curved spaces. The research aims to develop new metric invariants that capture the geometry of graphs and characterize local and asymptotic properties of Banach spaces. The project will...
- This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $111,427 to the University of Texas at Austin to study locally homogeneous geometric manifolds and their symmetry groups. The research aims to better understand special types of these mathematical objects, which have applications across mathematics and physics. The award will fund graduate student training and undergraduate research projects related to these...
This Project Grant award from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) totaling $150,000 will fund research at Texas A&M University from August 1, 2025 to July 31, 2027. The project is focused on studying a family of 3-manifold invariants constructed from the Virasoro Topological Quantum Field Theory (TQFT) and their asymptotic behavior, as well as investigating properties of fundamental shadow link complements. The research aims to advance the understanding of the connections between quantum topology, geometric topology, and mathematical physics. In addition to the core research, the project includes an educational component to enhance the training of young mathematicians in these areas through conferences and other activities. This award reflects NSF's mission to advance scientific knowledge and support transformative research with potential for broad societal impacts.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $150.0k | 7/17/25 |