Denis Osin, Vanderbilt University,

I will talk about a generalization of relative hyperbolicity based on the notion of a hyperbolically embedded subgroup. Examples of such subgroups include peripheral subgroups of relatively hyperbolic groups. They also appear in many other groups acting "nicely" on hyperbolic spaces (e.g. mapping class groups, outer automorphism
groups of free groups, and groups acting on trees). A substantial part of the theory of relatively hyperbolic groups can be generalized in the new context. As an applications we will solve some open problems about mapping class groups.