The group of automorphisms of the shift dynamical system and the Higman-Thompson groups

Abstract: 

We give a survey of recent results exploring connections between the Higman-Thompson groups and their automorphism groups and the group of automorphisms of the shift dynamical system. Our survey takes us from dynamical systems to group theory via groups of homeomorphisms with a segue through combinatorics, in particular, de Bruijn graphs.Joint work with Collin Bleak and Peter Cameron.