Research Group:

## The Femi-Pasta-Ulam-Tsingou problem: new developments in the framework of the Wave Turbulence Theory

## Riemann surfaces and integrable systems

**Content:**

Part 1

1.1Short review of the classical theory of finite-dimensional integrable systems

1.2 Be-Hamiltonian Geometry and Lax pair

1.3 The Toda system

1.4 The Korteweg de Vries equation: direct and inverse scattering on the line with decreasing initial data

1.5 Long time asymptotic for the solution of the KdV equation with decreasing initial data and Deift-Zhou steepest descent method

1.6 The Cauchy problem for the KdV equation with periodic initial data and action-angle variables.