Hypocoercivity is a concept introduced by C. Villani. It aims to give quantitative estimates for the convergence to equilibrium of hypoelliptic models. In this last lecture, I present an approach to hypocoercivity which parallels the Bakry-Emery approach to hypercontractivity. It is only based on local computations and provides quite explicit convergence rates.

The lecture is based on section 7 of the Lecture Notes.