Self-similar group actions and KMS states

Abstract: 

A self-similar action (G,X) consists of a group G along with a self-similar action of the group on a rooted tree. Self-similarity is displayed by the action of the group acting on all levels of the tree, in a similar fashion to fractals where patterns are repeated at all scales. Self-similar actions give rise to Cuntz-Pimsner algebras, first constructed by Nekrashevych, as well as a universal Toeplitz algebra. We describe KMS states on these algebras and how they give rise to a new trace on the group algebra. The presentation will be primarily focused on examples and is intended to be accessible to a pure mathematics audience.