September 16 and 23: Ivan Danilenko

Title: Slices of the Affine Grassmannian and Quantum Cohomology

Abstract:

The Affine Grassmannian is an ind-scheme associated to a reductive group $G$. It has a cell structure similar to the one in the usual Grassmannian. Transversal slices to these cells give an interesting family of Poisson varieties. Some of them admit a smooth symplectic resolution and have an interesting geometry related to the representation theory of the Langlands dual group. We will focus on equivariant cohomology of such resolutions and will show how the Knizhnik-Zamolodchikov equation arises as a quantum difference equation in this setting.