Yixuan Li:Homological Mirror Symmetry for Affine Grassmannian Slices in Type A

Abstract: This is joint work with Mina Aganagic, Ivan Danilenko, Vivek Shende and Peng Zhou. In this talk we discuss a homological mirror symmetry result, where both the symplectic side and the algebraic side are related to affine grassmannian slices in type A. Type A Affine grassmannian slices are useful geometric objects for studying representation theory. They include all type A Slodowy slices.  By the geometric Satake theorem, their homologies are related to weight spaces in tensor products of fundamental representations. Since Fukaya category can be loosely viewed as a categorification of the middle homology, this result can be viewed as one step towards two different categorifications of the geometric Satake theorem.