An introduction to warped cones

Warped cones are families of metric spaces that can be associated with actions of discrete groups on compact metric spaces. They were first introduced by John Roe as means of producing interesting examples of metric spaces (in the context of the coarse Baum-Connes conjecture), and have since evolved as it turned out that they could be used to construct families of expander graphs and that they were good candidates for a definition of a `coarse geometric’ invariant of actions. In this talk I will introduce the warped cone construction and explain how to use it to obtain expanders. I will then indicate some rigidity results that hold in this settings.