Isaac Newton Institute for Mathematical Sciences

Self-similar graphs, algebras and fractals

24th May 2007

Author: Volodymyr Nekrashevych (Texas A&M University)


We will discuss operator algebras associated with self-similar objects such as graphs, groups and dynamical systems. In particular, we will show how to reconstruct the Julia set of a rational function from its iterated monodromy group (or from the associated countable graph)using C*-algebras. We will also present a formula for the Hausdorff dimension of the Julia set, which suggests that this approach might be useful for constructing (quantized?) calculus on Julia sets.