Make Like a Graph and Split

Tuesday, 19-September-2023 

Abstract

In symbolic dynamics, shift spaces are used to approximate topological (or smooth) dynamical systems by using an alphabet of symbols to represent states of the system. In the 1970s, Williams showed that two shifts of finite type are conjugate if and only if we can get from one to the other using a series of "in-splits" and "out-splits" of their associated directed graphs. In this talk I aim to give a fresh perspective on splittings for directed graphs. I'll also show how this perspective lends itself to splittings of more general dynamical systems, including topological graphs and those arising in the noncommutative world of C*-dynamics.

This talk is based on recent work with Kevin Brix and Adam Rennie