# Chromatic aberrations of the geometric Satake equivalence

### APA

Devalapurkar, S. (2023). Chromatic aberrations of the geometric Satake equivalence. Perimeter Institute. https://pirsa.org/23040005

### MLA

Devalapurkar, Sanath. Chromatic aberrations of the geometric Satake equivalence. Perimeter Institute, Apr. 14, 2023, https://pirsa.org/23040005

### BibTex

@misc{ pirsa_PIRSA:23040005, doi = {10.48660/23040005}, url = {https://pirsa.org/23040005}, author = {Devalapurkar, Sanath}, keywords = {Mathematical physics}, language = {en}, title = {Chromatic aberrations of the geometric Satake equivalence}, publisher = {Perimeter Institute}, year = {2023}, month = {apr}, note = {PIRSA:23040005 see, \url{https://pirsa.org}} }

Sanath Devalapurkar Harvard University

## 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