This Project Grant award of $193,010.00 from the National Science Foundation's (NSF) Division of Mathematical Sciences under the CFDA 47.049 Mathematical and Physical Sciences program supports research to develop connections between number theory and physics. The project aims to explore the representation theory of quantum groups and their applications in explaining the bridge between special functions in number theory and statistical mechanics. The research will provide training opportunities...
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 $105,981 project grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research at the intersection of number theory, representation theory, and geometry. The research aims to explore geometric techniques in representation theory, with a focus on connections between representations of reductive algebraic groups over local fields and geometric constructions like...
This National Science Foundation (NSF) Project Grant award for $225,000 will fund the research activities of Professor Oscar Varela at Utah State University (USU) from August 1, 2023 to July 31, 2026. The research project aims to explore the relationship between general relativity and quantum field theory, with the goal of reconciling these seemingly disparate theories as complementary manifestations of an overarching set of physical principles. Key technical aspects of the project include...
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 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) awarded a $138,082 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to the University of Oregon. The grant supports fundamental and applied research in the areas of classical representation theory and categorification, including the study of symmetric groups, general linear groups, and related mathematical structures. The research aims to develop the theory of quiver Hecke superalgebras and apply it to improve...
The National Science Foundation (NSF) awarded a $180,000 Project Grant to the University of Southern California (USC) Department of Contracts and Grants Division under the Mathematical and Physical Sciences (CFDA 47.049) program. The 3-year grant will support research on "Combinatorial Representation Theory of Quantum Groups and Coinvariant Algebras." The project aims to further develop combinatorial diagrams called "web bases" that encode the representation category of...
The National Science Foundation (NSF) awarded a $155,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) Federal Grant Program to the University of Georgia Research Foundation, Inc. This funding supports research related to the representation theory of groups, which is the study of symmetry and its applications in various mathematical fields. The project aims to construct and classify pre-Tannakian categories, which are algebraic structures generalizing the...
This Project Grant from the National Science Foundation's Division of Mathematical Sciences provides $169,979 to Haverford College under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) from June 2022 through May 2025. The award will support research addressing two topics in the algebra, geometry, and representation theory of reductive algebraic groups over non-Archimedean local fields. Specifically, the investigator will apply techniques from geometric group theory...