## Mirror symmetry on the Hitchin system

## Working Seminar

Organized by

Tom Sutherland (FCUL, U. Lisboa) and

Emilio Franco (CAMGSD, IST, U. Lisboa).

The purpose of this working seminar is to provide an introduction to the Mirror Symmetry conjecture in the framework of the Hitchin integrable system, as a classical limit of the

Geometric Langlands program.

To this end, we will revise the following topics during the sessions of the working seminar:

- Derived category of sheaves and Fourier-Mukai transforms
- Moduli theory for Higgs bundles and non-abelian Hodge correspondence
- The Hitchin fibration and SYZ approach to Mirror symmetry
- Kapustin and Witten's approach to Geometric Langlands program

## Schedule of the talks

**Wednesday 6th November 15:00-16:00**, IST.

*Introduction to Mirror Symmetry on the Hitchin system* (by Emilio Franco).

This talk at the Geometria em Lisboa seminar will serve as an introduction to the whole minicourse. Here, we will briefly describe the geometrical objects involved in the Mirror conjecture on the Hitchin system and provide a motivation for it coming from mathematical physics. We will also sketch the structure of the working seminar and explain the approach we shall take.