Homology of affine Grassmannian and quantum cohomology

Abstract: Let G be a simply connected complex linear algebraic group, and X be a smooth projective G-variety. In this talk, we will construct an action of the equivariant homology of the affine Grassmannian Gr_G on the G-equivariant quantum cohomology of X. The construction uses shift operators in quantum cohomologies. When G=SL(2) and X is the projective line, this action is compatible with the Peterson isomorphism. Joint work with Alexander Braverman.