# Representation theory, gauge theory, and integrable systems

3-8 February 2019
Lecture Hall(1F), Kavli IPMU
Asia/Tokyo timezone

## Symplectic duality and Langlands duality

8 Feb 2019, 11:00
1h
Lecture Hall(1F), Kavli IPMU

Justin Hilburn

### Description

In this talk I would like to sketch how one can use the tools of derived symplectic geometry and holomorphically twisted gauge theories to derive a relationship between symplectic duality and local Langlands. Our starting point will be an observation due to Gaiotto-Witten that a $3d$ $\mathcal{N}=4$ theory with a $G$ flavor symmetry is a boundary condition for $4d$ $\mathcal{N}=4$ SYM with gauge group $G$. By examining the relationship between boundary observables and bulk lines we will be able to derive constructions originally due to Braverman, Finkelberg, Nakajima. By examine the relationship between boundary lines and bulk surface operators one can derive new connections to local geometric Langlands.

This is based on joint work with Philsang Yoo, Tudor Dimofte, and Davide Gaiotto.

### Presentation Materials

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