Project Grant H982300910049

This three-year, $207,196 project grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports research into the representation theory of finite reductive groups at the Massachusetts Institute of Technology. Specifically, the principal investigator will investigate new approaches to representations of Weyl groups and unipotent representations using a novel basis for the Grothendieck group. Additionally, the investigator will develop a new...

This Project Grant from the National Science Foundation's Mathematical and Physical Sciences program provides $325,855 to the University of Houston from June 2022 through May 2025. The funding supports research and training opportunities for graduate students in the theory of operator algebras generated by unitary group representations and their connections to discrete group structure. Specifically, the principal investigator will investigate new operator algebraic rigidity phenomena for...

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...

This $123,410 National Science Foundation project grant supports research into finite group actions on free resolutions at Cleveland State University from August 2022 through July 2025. The principal investigator will describe Betti numbers of polynomial equation systems with inherent symmetries, relying on computational algorithms. Graduate students will be involved in collecting and analyzing data to gain research experience alongside advanced mathematics learning. The goal is to describe...

This three-year National Science Foundation Project Grant of $378,000 will support research into boundaries of groups in geometric group theory and hyperbolic geometry at the University of Illinois at Chicago from September 2022 through August 2025. Specifically, the principal investigator and collaborators will investigate the Cannon Conjecture regarding differences between classical and Gromov hyperbolic geometry in three dimensions in the presence of symmetries. They will continue...

This National Science Foundation Project Grant award of $315,130 provides funding from September 1, 2022 through August 31, 2024 to support research on topological symmetries of non-compact Riemann surfaces. The award is made under the Mathematical and Physical Sciences program (CFDA 47.049) to the Research Foundation of the City University of New York on behalf of Queens College. The principal investigator will conduct research focusing on understanding the algebraic structure of mapping...

This three-year Project Grant from the National Science Foundation's Mathematical and Physical Sciences program ($160,000) will support research at Michigan State University exploring the connections between cluster algebras, quantum groups, and decorated character varieties. The principal investigator will investigate the quantum geometry of moduli spaces within the framework of cluster algebras, examining relationships between decorated character varieties, quantum groups, and Legendrian...

This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research on algebraic cycles, automorphic forms, and L-functions. The $230,000 award to The Trustees of Columbia University in the City of New York, spanning July 1, 2024 to June 30, 2027, aims to deepen the understanding of these mathematical objects and their connections, particularly in high dimensions. The research will include work on the...

This National Science Foundation award under the Mathematical and Physical Sciences program (CFDA 47.049) provides $275,396 to the University of Oklahoma from August 1, 2023 through July 31, 2026. The funding supports research into the geometries and topologies of surfaces and graphs. Specifically, the award will advance understanding of how abstract algebraic groups manifest as symmetries of geometric spaces in one and two dimensions. Graduate students will gain research experience applying...

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...