Fox and Hedgehog Seminar - 'Self-similar actions and their limit spaces'

A self-similar group (G,X) consists of a group G acting faithfully on a homogeneous rooted tree such that the action satisfies a self-similarity condition. In this talk I will introduce a beautiful theorem of Nekrashevych: there is a self-similar group associated to every post critically finite rational function whose limit space recovers the Julia set of the function. I’ll then show how I’ve used limit spaces of self-similar actions in other contexts to understand dynamical systems.