Abstract. This is a joint work with Linhui Shen.

A decorated surface is an oriented surface with punctures and a finite collection of special points on the boundary, considered modulo isotopy.

Let G be a split adjoint group. We introduce a moduli space Loc(G,S) of G-local systems on a decorated surface S, which reduces to the character variety when S has no boundary, and quantize it.

To quantize it, we consider a closely related moduli space P(G,S) and prove that it has a cluster Poisson structure, equivariant under the action of a discrete group containing the mapping class group of S, the product of the Weyl groups over the punctures of S, and the product of the braid group over the boundary components.

We will explain some applications to representation theory of quantum groups and Virasoro and W-algebras related to G.

## Date:

Monday, 1 April, 2019 - 16:00 to 18:00

Repeats every week every Monday until Mon Apr 29 2019 except Mon Apr 22 2019

## Location:

Ross 70