Chromatic aberrations of the geometric Satake equivalence

Abstract

The (derived) geometric Satake equivalence plays a central role in the geometric Langlands program: roughly, it describes the category of constructible sheaves of C-vector spaces on Bun_G(S^2) in terms of the Langlands dual group G^. In this talk, I will describe some ideas connecting chromatic homotopy theory to the derived geometric Satake equivalence. For example, we will describe the category of locally constant sheaves of A-modules on Bun_G(S^2), where A is complex K-theory or an elliptic cohomology theory, in Langlands
dual terms. Some of this work was motivated by considerations from physics, and I hope to say what little I know about this, as well as sketch its relationship to the Ben-Zvi-Sakellaridis-Venkatesh program.

Zoom Link:  https://pitp.zoom.us/j/94926220665?pwd=bVZFUFlvZGxVSG0xUFc1SGNaTDBKZz09