This National Science Foundation Division of Mathematical Sciences Project Grant of $322,321 provides funding from September 15, 2022 through August 31, 2025 to support collaborative research in the area of symplectic geometry between investigators at the University of Illinois. The research focuses on the momentum map and its applications to questions regarding symmetries and invariants in symplectic geometry. Key areas of focus include the equivariant geometry of symplectic four-manifolds, applications of equivariant theory to symplectic topology, complexity one Hamiltonian torus actions, completely integrable systems, and the geometry and topology of momentum maps. The grant also supports mentorship of graduate students and postdoctoral fellows, as well as outreach activities to promote mathematics education. This award furthers the Mathematical and Physical Sciences program's goals of advancing scientific knowledge and understanding in major problem areas through support of basic research and related activities.
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