March 4 : Ivan Danilenko

Title: Slices of the Affine Grassmannian and Quantum Cohomology

Abstract: The affine Grassmannian is a space constructed from the loop group of a reductive group $G$ in a way similar to how the usual Grassmannian is constructed from $G$ itself. We are interested in the geometric properties of a family of symplectic resolutions naturallyappearing from transversal slices to Schubert-like cells in the affine Grassmannian. By the geometric Satake correspondence, one can work with certain geometric objects called perverse sheaves and their cohomology using the representation theory of the Langlands dual group $G^\vee$. We use this to present the computations in a clearer way.