◆ Lecture 1 : Heuristics, history and preparations
◆ Lecture 2 : Nonlinear proof, following Mouhot-Villani
◆ Lecture 3 : Extensions, refinements, criticality, following Bedrossian-Masmoudi-Mouhot
In 2010, Clément Mouhot and I proposed a solution of the nonlinear Landau damping problem, the celebrated effect according to which a homogeneous equilibrium of a plasma may be nonlinearly stable through mixing, confinement and regularity. One of the key ingredients was an analogy with the well-known Kolmogorov-Arnold-Moser theory, through the study of plasma echoes. After that, the proof was revisited and extended by Jacob Bedrossian, Nader Masmoudi and Clément Mouhot. These lectures will survey the whole story. Some conjectures will be reviewed.
