Project Grant 2502205
- 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 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...
- The National Science Foundation (NSF) awarded a $150,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to the Georgia Tech Research Corporation. The grant, awarded on September 15, 2025, will support a research project investigating important problems in quantum topology and its connections with classical topology and hyperbolic geometry. The project aims to advance the understanding of three- and four-dimensional topology and knot theory, which...
- 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...
- This Project Grant award, provided by the National Science Foundation (NSF) under its Mathematical and Physical Sciences program (CFDA 47.049), supports research and education to advance the understanding of quantum geometric effects in interacting electron systems, with a focus on topological insulators. The $270,000 award, spanning from September 1, 2025 to August 31, 2027, will investigate the interplay of quantum geometry, band topology, and electron interactions in topological materials....
- 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 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 federal Project Grant award of $150,000 from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) aims to explore the connections between algebraic topology, quantum algebra, and statistical problems in arithmetic. The primary goals are to use algebro-topological tools to address open questions in quantum algebras and to leverage these tools, along with the Weil conjectures, to enumerate points on moduli spaces over finite fields. This work has...
- This $330,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research into quantum groups, W-algebras, and Brauer-Kauffmann categories, with a focus on understanding the underlying mathematical symmetries that govern natural phenomena. The principal investigator will develop emerging theories and applications of I-quantum groups, including exploring braid group actions, Drinfeld presentations, and...
- This $150,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on two open problems in algebraic combinatorics that intersect representation theory and algebraic geometry. The principal investigator and collaborators aim to use combinatorics to better understand these abstract mathematical objects in a more concrete way, with potential applications in mathematics, physics, and human-machine...
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 polynomial, aiming to establish improved functoriality properties by reinterpreting it in the setting of sutured 3-manifolds. This research is expected to shed light on related quantum theories, such as Chern-Simons theories used in topological quantum computing. The project will also provide research training opportunities for graduate students. The award period runs from September 1, 2025 to August 31, 2027.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $120.3k | 8/1/25 |