# Fundamental local equivalences in quantum geometric Langlands

### APA

Dhillon, G. (2020). Fundamental local equivalences in quantum geometric Langlands. Perimeter Institute. https://pirsa.org/20060038

### MLA

Dhillon, Gurbir. Fundamental local equivalences in quantum geometric Langlands. Perimeter Institute, Jun. 22, 2020, https://pirsa.org/20060038

### BibTex

@misc{ pirsa_PIRSA:20060038, doi = {10.48660/20060038}, url = {https://pirsa.org/20060038}, author = {Dhillon, Gurbir}, keywords = {Mathematical physics}, language = {en}, title = {Fundamental local equivalences in quantum geometric Langlands}, publisher = {Perimeter Institute}, year = {2020}, month = {jun}, note = {PIRSA:20060038 see, \url{https://pirsa.org}} }

Stanford University

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Abstract

In quantum geometric Langlands, the Satake equivalence plays a less prominent role than in the classical theory. Gaitsgory--Lurie proposed a conjectural substitute, later termed the fundamental local equivalence, relating categories of arc-integrable Kac--Moody representations and Whittaker D-modules on the affine Grassmannian. With a few exceptions, we verified this conjecture non-factorizably, as well as its extension to the affine flag variety. This is a report on joint work with Justin Campbell and Sam Raskin.