# Laure Saint-Raymond

Laure Saint-Raymond
(Ecole normale supérieure de Lyon)

#### Title: Dynamics of a Hard Sphere Gas

Consider the Hamiltonian dynamics of a system of hard spheres, such as billiard balls or marbles. In the kinetic limit (when the number of spheres tends to infinity), the system is described by the  Boltzmann equation which is irreversible. As the microscopic dynamics is reversible, this may be seen as a paradox. We will explain that the emergence of the irreversibility in the kinetic limit is related to singular dynamical correlations with an intricate structure going through all scales. We shall discuss the combinatorial techniques that can help analysing the departure from chaos.