This three-year, $611,884 project grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports collaborative research on higher categorical structures in algebraic geometry at Northwestern University from September 2022 through August 2025. The project aims to apply recent developments in higher category theory and condensed mathematics to longstanding questions in algebra and algebraic geometry relating to complete noncommutative categorical...
This $300,000 Project Grant award, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), supports research at Stanford University to develop a new framework for studying algebraic structures in topology. The key technical focus is on formulating algebraic structures geometrically at the level of underlying "flow categories" in order to extend applications of Floer homotopy theory to areas like symplectic and...
This three-year Project Grant from the National Science Foundation Division of Mathematical Sciences, totaling $540,974, will fund collaborative research applying recent developments in higher category theory and condensed mathematics to longstanding questions in algebraic geometry and the introduction of new questions in analytic algebraic geometry. Specifically, the principal investigators and their collaborators at the University of California, Berkeley will pursue four main research...
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 $106,185 federal Project Grant award from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) supports research at The Johns Hopkins University to advance the Langlands Functoriality Conjecture. The project aims to use quantization methods to construct novel ways of comparing relative trace formulas, which have important applications in number theory. Key expected products include new mathematical techniques for proving functoriality conjectures, as well as...
The National Science Foundation (NSF) awarded a $405,500 Project Grant under its Mathematical and Physical Sciences (CFDA 47.049) program to Duke University to support a research program in A1-homotopy theory and its applications to enumerative geometry and number theory. The award will fund research to develop enriched counting methods that can detect differences in the number of solutions to equations requiring real or imaginary numbers, with potential applications in number theory and...
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 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides $318,144.00 to the University of Notre Dame DU Lac to advance research in the field of delocalized homotopy theory. The goal is to develop new computational tools in algebraic topology to better understand the topological properties of geometric objects. Key activities include completing the analysis of K(2)-local homotopy groups, investigating generalizations...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research into classical representation theory and categorification. The $138,082 award to the University of Oregon, with a performance period from August 15, 2024 to July 31, 2027, will fund research on mathematical objects like symmetric groups and general linear groups, and their representation theory. The project aims to further develop the theory of...
This Project Grant award from the National Science Foundation's (NSF) Computer and Information Science and Engineering (CISE) program, with CFDA Number 47.070, provides $234,236 to The University of Iowa to develop new foundations for machine-verified proof in programming languages and mathematics. The project will create a novel impredicative dependent row type theory that enables greater proof modularity, reuse, and extensibility across different theorem proving systems and logics. This will...