This $138,082 federal Project Grant award from the National Science Foundation's (NSF) Division of Mathematical Sciences (CFDA 47.049 - Mathematical and Physical Sciences) will support research and development at the University of Oregon (UO) from August 15, 2024 to July 31, 2027. The key objectives of this award are to advance the understanding of classical representation theory and categorification, with a focus on studying the symmetries of finite sets and vector spaces through the lens of...
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 $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 awarded a $270,540 project grant to the University of Oregon from July 2021 through June 2024 under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports research into modular representation theory and categorification with applications. The University of Oregon will conduct theoretical and applied work in these areas over the three year period. Representation theory and categorification are mathematical tools with uses across physics,...
The National Science Foundation awarded a $260,633 project grant to the University of Oregon under the Mathematical and Physical Sciences program (CFDA 47.049) for work on "Graphical and Categorical Methods in Representation Theory." The three-year award beginning July 1, 2021 will support research using graphical and categorical techniques to further understanding of representation theory, a branch of mathematics that studies symmetry in linear algebra and its applications. As the...
This Project Grant award of $149,002 was provided by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049). The award will fund research at the University of Iowa to extend the foundations of representation theory of finite dimensional associative algebras to the setting of algebras in tensor categories. This work aims to broaden participation in mathematics by engaging a diverse group of doctoral students in...
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 $343,286 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of Oregon. The three-year grant, starting on August 1, 2024, supports research on C*-algebras and dynamics beyond the Elliott classification program. The key objectives are to investigate when simple C*-algebras, a type of mathematical object with applications in quantum mechanics, are isomorphic to their opposite algebras. The project aims...
This National Science Foundation (NSF) Division of Mathematical Sciences grant award, titled "Categorical Centers, Cactus Actions, and Diagram Algebras," provides $170,000 in funding to Northeastern University over 3 years, from September 1, 2023 to August 31, 2026. The project will develop a deeper understanding of representation theory, which studies the symmetries of mathematical objects, by combining algebraic, combinatorial, and categorical techniques to investigate quantum groups...
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...