Geometric Satake Revisited

The geometric Satake equivalence is a fundamental result in the geometric Langlands program. It can be understood as a kind of Fourier transform, relating different flavors of sheaves on a dual pair of spaces. Just like the usual Fourier transform, the equivalence exchanges the structures of convolution and pointwise product on each side. In this talk, I will give an informal and accessible overview of this part of the geometric Langlands program and discuss a circle of ideas relating pointwise tensor product of sheaves on the affine Grassmannian, the Knop-Ngo action for the group scheme of regular centralizers, and Moore-Tachikawa varieties. This builds on past joint work with D. Ben-Zvi and some current work in progress with D. Ben-Zvi and S. Devalapurkar.