**Speaker:** Laure Saint-Raymond, Professor of Mathematics at Pierre and Marie Curie University (Paris VI) and École Normale Supérieure

A series of three lectures entitled **From Particle Systems to Kinetic Equations.**

**Lecture II: A short time convergence result**

Lanford's theorem states that in the Boltzmann-Grad limit the one-particle density converges to the solution of the kinetic Boltzmann equation almost everywhere on a short time interval (corresponding actually to a fraction of the average first collision time). The proof relies on a careful study of the recollision mechanism (which is not described by the Boltzmann dynamics), and on a priori bounds obtained by a Cauchy-Kowalewski argument. In the second lecture, we will give a sketch of this proof, and show that the time restriction is due to the lack of global a priori bounds.