The National Science Foundation (NSF) awarded a $149,329 Project Grant under its Integrative Activities (IA) program to Louisiana State University (LSU) on July 1, 2024. The grant will fund research exploring the rich interplay between geometric representation theory, algebraic combinatorics, algebraic geometry, mathematical physics, and symplectic geometry. Specifically, the project aims to: 1) introduce a new class of additive analogues of spherical varieties using Poisson-Lie group theory, 2) explore matroid Schubert varieties and their connections to toric geometry, and 3) develop new links between Poisson geometry and symplectic representation theory by studying groupoids associated with symplectic resolutions. The project will also provide research training opportunities for graduate students. No sub-awards are planned under this grant.
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