First lecture by Thi Ndang.

Title: Uniform subexponential chaos

Abstract: Let G be a real simple Lie group of finite center, M a smooth compact manifold and D<G a cocompact lattice acting by smooth diffeomorphism on M. Provided that the dimension of M is bounded by the rank of G or the action is volume preserving, Brown Fisher and Hurtado recently proved that such an action of D by diffeomorphism must be trivial.
I'll start by introducing the main blocks in their proof starting by the notion of uniform subexponential chaos (USC).
I'll prove that this more deterministic concept is equivalent to the cancellation of all Lyapunov exponents (who are random beings).

Second lecture by Alessandro Carderi.

Title: An introduction to orbit equivalence

Abstract: In this second lecture we are going to study probability measure preserving actions of countable groups under the point of view of orbit equivalence. We will discuss about the Bernoulli shift which will be the main object in the second part of this lecture series. We will give a bit of history about orbit equivalence and present some important results. Finally we will properly state the main theorem of this course and discuss about one of its important corollaries.