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...
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 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 $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...
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...
This federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $210,000.00 to the University of Oregon (UO) to conduct research on the "Categorification of Quasi-Split I-Quantum Groups and Related Topics in Representation Theory". The project aims to take the next step in categorifying all quasi-split I-quantum groups, building on recent discoveries by the principal investigator and collaborators. The...
This $119,497 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research at the intersection of combinatorics, algebra, geometry, and topology. The principal investigator will use combinatorial models to study representation theory, Lie algebra representations, and the Schubert calculus on flag manifolds. Key research objectives include developing new applications and problems involving crystals, extending the...
This federal Project Grant award, valued at $138,082, was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049) to the University of Oregon. The award supports fundamental and applied research in representation theory, categorification, and higher symmetries, with potential future impact in theoretical physics and computer science. The research project will develop the theory of quiver Hecke superalgebras and apply it...
This $257,995 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research at the University of Iowa to advance the understanding of von Neumann algebras and their connections to other mathematical fields. The project will develop new techniques at the intersection of deformation/rigidity theory, group theory, ergodic theory, and continuous model theory to address fundamental open problems in the classification 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...