Regularity of Solutions for Some Degenerate Equations

In this talk, I would report recent results on the Gevrey (or analytic) regularities of solutions for some degenerate paritial differential equations, including (1) generalised Kolmogorov equations (or linear Boltzmann equations), (2) Fokker-Planck equations, (3) Landau equations and (4) sub-elliptic Monge-Ampere equations.