D. Osin

13 - 17 May

Title: Acylindrically hyperbolic groups.

Abstract:

We will discuss recent progress in the study of groups acting on hyperbolic spaces. Specifically, we will focus on acylindrically hyperbolic groups and their hyperbolically embedded subgroups. The class of acylindrically hyperbolic groups is very wide and includes many examples of interest, yet the property of being acylindrically hyperbolic is strong enough to allow one to derive deep results. In particular, many aspects of the theory of relatively hyperbolic groups, including group theoretic Dehn filling and small cancellation methods, can be generalized to acylindrically hyperbolic groups using the notion of a hyperbolically embedded collection of subgroups. We will also discuss some open questions.