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**Video URL**
http://pirsa.org/22060091

## Abstract

I will discuss a close parallel between Gaiotto and Witten's S-duality for supersymmetric boundary conditions in 4d N=4 SYM and the relative Langlands program, an enhancement of the Langlands program that was developed to provide a framework for the theory of integral representations of L-functions. A special and conjecturally self-dual class of boundary conditions is provided by quantizations of "small" or "multiplicity-free" hamiltonian spaces called hyperspherical varieties. I'll explain how a hyperspherical variety produces objects of interest in all the different settings of the Langlands program (local / global, geometric / arithmetic) and a collection of conjectures providing S-dual descriptions of these objects. The talk is based on forthcoming joint work with Yiannis Sakellaridis and Akshay Venkatesh.

## Details

**Talk Number**22060091

**Speaker Profile**David Ben-Zvi

**Collection**QFT for Mathematicians 2022

- Mathematical physics

**Scientific Area**

- Conference

**Talk Type**

**Subject**Mathematical Physics

**Source Repository**PIRSA