Geometric Satake equivalence for Kac-Moody groups

The goal of the talk is to describe a geometric Satake equivalence for affine Kac-Moody groups as an equivalence of abelian semisimple categories. To do this, we define a well-behaved category of equivariant sheaves on the double affine Grassmaniann that is equipped with a t-structure. Then, we prove an hyperbolic localization theorem for such a stack and prove that the constant term functor is t-exact.