Automorphism Groups and Tensor Products of Bratteli Diagrams

Andrew Barsky

Since the 1990s, Bratteli Diagrams have been a major tool in studying topological dynamics, by way of the Vershik map. This allows us to study actions of Z on the Cantor set. In this talk I look at some constructions that allow us to consider more general group actions on the Cantor set using Bratteli diagrams. First, treating Bratteli diagrams just as a graph, we can consider the graph automorphisms; these wind up also inducing homeomorphisms on the path space. Then, I will introduce a tensor product construction (the diagram that we get by looking at the tensor products of incidence matrices of two different Bratteli diagrams), which lets us model some Z^n actions using Vershik maps. This talk is based on joint work with Sergii Bezuglyi.

To participate in this event virtually via Zoom, go to https://uiowa.zoom.us/j/95316149275.