On group actions and expansion

The theme of this talk is on the interplay between dynamics and large scale geometry (with a view towards applications in operator algebras).
I will begin by overviewing some not-so-recent connections between group actions on compact manifolds and expander graphs, and explain how they arise from the study of a geometric construct known as warped cone.
Further following this train of thoughts we can also find similar phenomena in more general settings. This path will lead us to more recent results and current research.