Ana Balibanu, Assistant Professor of Mathematics at LSU, has been awarded a three-year research grant from the US National Science Foundation (NSF). Titled "Wonderful Varieties, Hyperplane Arrangements, and Poisson Representation Theory," the grant supports a project that investigates the algebraic structures arising from the symmetries of geometric objects. This research is expected to advance knowledge in several fields, including algebraic combinatorics, algebraic geometry, mathematical physics, and symplectic geometry. Additionally, the project will develop new representation-theoretic constructs and provide comprehensive research training opportunities for graduate students.

The project will address three interconnected problems. The first problem focuses on developing a new class of additive analogues of spherical varieties, constructed through degenerations influenced by the theory of Poisson-Lie groups. The second problem will explore matroid Schubert varieties and their links to toric geometry, aiming to deepen understanding in this area. Lastly, the project seeks to forge new connections between Poisson geometry and symplectic representation theory by analyzing groupoids associated with symplectic resolutions.