String-Math Seminar: Slices of the Affine Grassmannian and Quantum Cohomology

Seminar | November 18 | 2-3 p.m. | 402 LeConte Hall

 Ivan Danilenko, Columbia University

 Department of Mathematics

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 trigonometric Knizhnik-Zamolodchikov equation arises as a quantum differential equation in this setting.