Lei Yang: Local rigidity of higher rank Abelian actions on nilmanifolds by partially hyperbolic automorphisms

Abstract: We will consider local rigidity of higher rank Abelian actions on compact nilmanifolds by partially hyperbolic automorphisms. We will prove that small perturbations are smoothly conjugate to the original action. The proof relies on a KAM iteration argument and the exponential mixing of the original action. This is a joint work with Ralf Spatzier.