Alex Weekes

Title: Affine Grassmannian slices and their categories O

Abstract:

One of the most important classes of spaces in geometric representation theory are the affine Grassmannians, whose geometry is intimately connected to the representations of Lie groups. In this talk I will discuss a manifestation of this connection: recent joint work studying categories of modules over deformation quantizations of affine Grassmannian slices, and connections to work of Khovanov-Lauda, Rouquier, and Webster on categorification of representations. This progress has been aided by Braverman-Finkelberg-Nakajima's realization of affine Grassmannian slices as Coulomb branches. This all works only in symmetric type; time permitting I will describe on-going work aiming to extend to symmetrizable types.

Joint with J. Kamnitzer, P. Tingley, B. Webster and O. Yacobi.