Additional Information

The topic will be Dynamics of Large Groups. The course will focus on continuous actions of non-locally compact groups that are equipped with a complete separable topology (Polish groups). This class of groups includes the unitary group of the separable Hilbert space, homeomorphism groups of compact metric spaces, automorphism groups of countable structures, and the group of measure preserving transformations, among others. The emphasis of the course will be on the structure of orbit equivalence relations and on the structure of continuous actions on compact spaces (flows). In addition to the general introduction to the subject, we will cover the following topics: (1) The Kechris-Louveau theorem identifying a fundamental obstacle for an equivalence relation to be an orbit equivalence relation. (2) Effros-type theorems on embedding of the Vitali equivalence relation into orbit equivalence relations. (3) Universal minimal flows.