# Mini-courses

**Damien Gaboriau**(École Normale Supérieure de Lyon)

**Title:**Measurable Group Theory.

**The goal of this series of lectures is to present an overview of the theory of orbit equivalence of measure preserving actions of countable groups, with a particular focus on the free groups. I will give several examples and explain some tools and invariants such as the theory of cost, the fundamental groups, measure equivalence of groups... I will present the framework for a measurable solution to the problem of von Neumann about non-amenability vs containment of a free subgroup.**

Abstract.

Abstract.

**Thierry Giordano**(University of Ottawa),

**Ian F. Putnam**(University of Victoria),

**Christian Skau**(Norwegian University of Science and Technology)

**Title**: Topological orbit equivalence and minimal dynamics on the Cantor set.

**Abstract:**We will give an overview of minimal dynamical systems on the Cantor set with the aim of describing a complete invariant for orbit equivalence of actions of finitely generated abelian groups. Of course, this builds heavily on the similar program in ergodic theory initiated by Henry Dye, but we will focus on the aspects which are different in the topological setting. Many of the tools and invariants have their origin in C*-algebra theory, but our approach will be completely dynamical.

**Kate Juschenko**(Northwestern University)

**Title:**Amenability and algebraic properties of the full topological groups.

**Abstract**. in four lectures we will present as complete as possible proof of the fact that the commutator subgroup of minimal subshift is simple, finitely generated, amenanle and there are uncountably many of such.

**David Kerr**(Texas A&M University)

**Title:**Sofic entropy.

**Abstract.**I will present the basic theory and major developments in the subject of

sofic entropy since its inception a little more than five years ago in the breakthrough

work of Lewis Bowen. I will also discuss how these ideas relate to the classical

Kolmogorov-Sinai picture of dynamical entropy, which applies most generally to actions

of amenable groups. Topics will include Gottschalk´s surjunctivity conjecture,

Bernoulli actions, algebraic actions, and the f-invariant.