# Geometric Representation Theory

Event Information Slices of the Affine Grassmannian and Quantum Cohomology
14:00 on Friday November 22, 2019
15:30 on Friday November 22, 2019
Stewart Library, Fields Institute, 222 College St.
Ivan Danilenko

Columbia University

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 $G^\vee$. We will focus on equivariant cohomology of such resolutions and will show how the trigonometric Knizhnik-Zamolodchikov equation arises as a quantum differential equation in this setting.