# Perverse sheaves and relative Langlands duality

### APA

Wang, J. (2021). Perverse sheaves and relative Langlands duality. Perimeter Institute. https://pirsa.org/21090015

### MLA

Wang, Jonathan. Perverse sheaves and relative Langlands duality. Perimeter Institute, Sep. 17, 2021, https://pirsa.org/21090015

### BibTex

@misc{ pirsa_21090015, doi = {10.48660/21090015}, url = {https://pirsa.org/21090015}, author = {Wang, Jonathan}, keywords = {Mathematical physics}, language = {en}, title = {Perverse sheaves and relative Langlands duality}, publisher = {Perimeter Institute}, year = {2021}, month = {sep}, note = {PIRSA:21090015 see, \url{https://pirsa.org}} }

Jonathan Wang Perimeter Institute for Theoretical Physics

## Abstract

The program of Ben-Zvi--Sakellaridis--Venkatesh connects the construction of L-functions in number theory with S-duality of boundary conditions in 4d. In particular this predicts certain equivalences of categories between equivariant D-modules on the formal loop space of a smooth variety X and equivariant quasi-coherent sheaves on a Hamiltonian manifold. I discuss an extension of this conjecture to certain singular varieties X and the possibility of quantizing the equivalence. I will explain joint work with Yiannis Sakellaridis on computing a certain factorization algebra which plays a role in the story.

Zoom Link: https://pitp.zoom.us/j/95543248994?pwd=bmZIRnEyLzZnNmlEWW5oNTEwaEhNUT09