Minicourse
Title: Spectral gap for smooth surface diffeomorphisms
Speaker: Omri Sarig (Weizmann Institute of Science)
Abstract: I will survey recent joint work with Jerome Buzzi and Sylvain Crovisier on the dynamics of smooth surface diffeomorphisms with positive topological entropy. The principal new idea is a dynamical property called "strong positive recurrence" (SPR), which holds for all smooth surface diffeomorphisms, and which implies in the positive topological entropy case the existence of a symbolic dynamical model with spectral gap. What this means will be explained in the minicourse. Spectral gap implies many stochastic and dynamical properties, e.g. exponential decay of correlations for the measure of maximal entropy.