The class of acylindrically hyperbolic groups has been of immense interest in recent times. It is an extremely large class of groups, containing many interesting examples. Yet a significant part of the theory of hyperbolic and relatively hyperbolic groups can be generalized in this context. The goal of this mini course is to provide an introduction to this class of groups, and focus on some important techniques.
In the first lecture, we will define acylindrical actions and talk about the motivation to study them. We will then define acylindrically hyperbolic groups and discuss some examples and properties of this class of groups. The second lecture will focus on the notion of hyperbolically embedded subgroups and discuss relative hyperbolicity in this context. In the last lecture, we will discuss the concept of group theoretic Dehn filling and some of its applications. Time permitting, I will also talk a bit about my own research.
These videos were part of the Geometric group theory without boundaries II virtual summer school.
