EVENT DETAILS AND ABSTRACT

Title: De Bruijn Automorphisms of the Full Shift
Speaker: Collin Bleak
Speaker Info: University of St Andrews
Brief Description:
Special Note:
Abstract:

We investigate a set of groups {SBC_n}. Each group SBC_n sits very naturally in the full group of automorphisms of {0,1, ... , n-1}^Z, the full shift on n letters, and is somehow a very natural object. Still, the structure of each group SBC_n, at least initially, was quite a mystery.

These groups' elements are describable as finite transducers, and so the groups SBC_n are linked strongly to the rational group R introduced by Grigorchuk, Nekrashevych, and Suschanskii. Furthermore, the group SBC_n corresponds precisely to the outer automorphism group of the generalized Higman-Thompson group G_{n,1} = V_n.

In this talk, we discuss and exploit a connection with De Bruijn graphs to begin to explore the structure of the groups SBC_n. We fully describe SBC_2, and we discuss the conjecture that SBC_n is actually Aut({0,1,...,n-1}^\omega), the automorphisms of the full one sided shift on n letters.

This talk features work from two separate projects involving collaborators Y. Maissel, A. Navas, and P. Cameron.