The stabilized automorphism group of a subshift

The automorphism group $Aut(\sigma)$ of a subshift $(X,\sigma)$ consists of all homeomorphisms $\phi\colon X\to X$ such that $\phi\sigma=\sigma\phi$. When $(X,\sigma)$ is a shift of finite type, $Aut(\sigma)$ is known to have a rich group structure, and we’ll discuss some background and problems related to the study of $Aut(\sigma)$. Finally, we’ll introduce a certain stabilized automorphism group and outline results which, among other things, provide new cases in which we can distinguish (up to isomorphism) the stabilized groups of certain full shifts. This is joint work with Yair Hartman and Bryna Kra.​