Project Grant 2604508
- The National Science Foundation Division of Mathematical Sciences awarded Northwestern University $175,000 on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop the theory of factorization homology for 3-manifolds with coefficients in rigid braided infinity-categories and to apply that theory to low-dimensional topology, topological quantum field theory, and representation theory. The project develops mathematical constructions that integrate...
- The National Science Foundation Division of Mathematical Sciences awarded Michigan State University $270,000 on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to study quantum topology and geometric structures in three-dimensional spaces. The research focuses on mathematical classification of three-dimensional manifolds and knotted structures within them, with particular emphasis on connections between quantum field theory and geometric properties. The...
- The National Science Foundation Division of Mathematical Sciences awarded Michigan State University $243,100 on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to conduct research on low-dimensional topology through Floer homology. The research investigates the classification and structure of three- and four-dimensional smooth manifolds using tools from gauge theory. The project explores homology cobordism groups, which enable three-manifolds to be studied...
- The National Science Foundation Division of Mathematical Sciences awarded New Mexico State University $192,000 on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop new equivariant homotopy theoretic tools for studying symmetries in geometric shapes through algebraic topology. The project expands the framework of Eulerian sequences—introduced under prior NSF support (DMS-2305016)—to construct equivariant Araki-Kudo-Dyer-Lashof operations on the...
- Montana State University received a $119,626 project grant award from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The two-year award, made on September 1, 2021 and concluding on August 31, 2023, will support the LEAPS-MPS: Elliptic Theory for the Schrodinger Operator project. Through this funding, Montana State University researchers will promote progress in mathematical and physical...
- This $280,444 National Science Foundation project grant supports research and education activities advancing the Langlands program for 3-manifolds at Montana State University from June 2022 through May 2025. Funded through the Integrative Activities program under the National Science Foundation's Division of Mathematical Sciences, the grant supports defining and studying the space of states associated with a 3-manifold in the family of geometric Langlands topological quantum field theories....
- This $200,000 National Science Foundation project grant supports mathematical and physical sciences research at Michigan State University from September 2022 through August 2025. The award falls under the Mathematical and Physical Sciences program (CFDA 47.049), which aims to advance scientific knowledge and address national problems through basic research and education in these fields. Specifically, the principal investigator and their team will investigate Floer and Khovanov theories...
- The National Science Foundation Division of Mathematical Sciences awarded The Washington University $243,100 on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop homological and persistence-based tools arising from gauge theory and apply them to fundamental problems in low-dimensional topology, including questions about knots and three-dimensional spaces. The project, titled "Instantons, Knots and Surgery," will advance instanton Floer...
- The National Science Foundation Division of Mathematical Sciences awarded The University of Kentucky Research Foundation $180,000 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop and apply mathematical tools for studying symmetry and cohomology in algebraic geometry, representation theory, and topology. The project centers on two primary research goals: computing stable cohomology of line bundles on flag varieties in arbitrary characteristic...
- The National Science Foundation Directorate for Mathematical and Physical Sciences awarded Montana State University $350,000 on August 15, 2026, to support collaborative research on exciton dynamics in chiral molecular nanowires under the Mathematical and Physical Sciences program (CFDA 47.049). Professor Erik Grumstrup at Montana State University and Professor Jean Hubert Olivier at the University of New Mexico are investigating how solid-state chirality influences exciton...
The National Science Foundation Division of Mathematical Sciences awarded Montana State University $195,993 on September 1, 2026, for collaborative research developing factorization homology, a mathematical construction that integrates complicated objects over three-dimensional space with applications to knot theory, topological quantum field theory, and representation theory. The project, funded under the Mathematical and Physical Sciences program (CFDA 47.049), advances the theory of factorization homology for three-manifolds with coefficients in rigid braided infinity-categories, with specific objectives including analysis of moduli spaces of graphs in three-manifolds, construction of cosheaves on these spaces, proof of the tangle hypothesis for singular one-dimensional tangles, and derivation of enhancements to conjectured Langlands duality for skein modules. The work integrates derived category theory into quantum topology and establishes new connections between moduli spaces of embedded manifolds and quantum systems. The project includes organization of workshops for early-career researchers and mentoring of post-doctorates and graduate students. Performance occurs in Bozeman, Montana, with a period of performance from September 1, 2026, through August 31, 2029.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $196.0k | 8/5/26 |