Hyperbolically Embedded Subgroups of Acylindrically Hyperbolic Groups - Lecture 3

Explore the third part of a lecture series on hyperbolically embedded subgroups of acylindrically hyperbolic groups. Delve into an introduction to acylindrically hyperbolic groups through the lens of hyperbolically embedded subgroups. Begin with definitions and examples before investigating the geometric and algebraic properties of these subgroups. Examine connections with random walks, extending actions, extending quasicocycles, and relative hyperbolicity. Learn about the power of hyperbolically embedded subgroups, particularly virtually cyclic ones, as tools for proving important results about acylindrically hyperbolic groups. Discover how these subgroups are utilized in proofs of significant theorems. No prior knowledge of these topics is required for this 51-minute lecture, part of the Workshop on Geometry of Subgroups held at the Centre de recherches mathématiques.