Research Group:

## Riemann surfaces and integrable systems

**Program of the course:**

## Integrable Systems

- Definition of an integrable system in finite dimension.
- Lax pair.
- Infinite dimensional integrable systems.
- An example: the Toda lattice equation. Soliton solution and periodic solutions.
- Toda lattice and Hermitian random matrices.
- The beta-ensamble (non integrable).