Acylindrically hyperbolic groups

Abstract

These are notes from a mini-course lectured by Denis Osin on acylindrically hyperbolic groups given at Beyond Hyperbolicity in Cambridge in June 2016. In this course we will be looking at acylindrically hyperbolic groups. Such groups make up a large portion of the "universe of finitely presented groups" described in Martin Bridson's course. Through examples of such groups we shall see that this class is indeed a large portion of the universe, but we shall also see that there is much we can prove. In particular, we will discuss results on small-cancellation theory and Dehn fillings, as well as some newer results.