Project Grant 2603192

Federal Project Grant Summary

Michigan State University received a $270,000 Project Grant from the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049), effective September 1, 2026 through August 31, 2029. The award supports fundamental research in quantum topology and geometric structures in three-dimensional spaces, with primary focus on classifying three-dimensional manifolds and understanding relationships between quantum topological field theories (TQFTs) and geometric properties of three-manifolds. The research employs methods from representation theory, hyperbolic geometry, and algebraic geometry to establish connections between quantum structures and geometric structures, with specific investigations into Witten-Reshetikhin-Turaev TQFTs, the Thurston norm, and the Seifert genus of knots.

In addition to advancing fundamental mathematical science addressing open conjectures in topology and physics, the grant provides professional development support for graduate student research, including mentoring and conference travel funding. The research outputs will contribute to understanding rigidity and flexibility properties (invariants) of three-dimensional spaces, with potential applications to fundamental physics and topology. The award is executed at Michigan State University's East Lansing, Michigan location.