A sequence of expanders is a family of finite graphs that are sparse yet highly connected. Such families of graphs are fundamental object that found a wealth of applications throughout mathematics and computer science. This talk is centred around an ‘asymptotic’ weakening of the notion of expansion. The original motivation for this asymptotic notion comes from the study of operator algebras associated with metric spaces. Further motivation comes from some recent works which established a connection between asymptotic expansion and strongly ergodic actions. I will give a non-technical introduction to this topic, highlighting the relations with usual expanders and group actions.
This video was produced by Newcastle University, Australia, as part of the Symmetries in Newcastle seminar series.
