Groups and Dynamics Seminar

Date: January 31, 2018

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Rostislav Grigorchuk, Texas A&M

Title: Group of intermediate growth, aperiodic order, and Schroedinger operators.

Abstract: I will explain how seemingly unrelated objects: the group G of intermediate growth constructed by the speaker in 1980, the aperioidc order, and the theory of (random) Schroediinger operator can meet together. The main result, to be discussed, is based on a joint work with D.Lenz and T.Nagnibeda. It show that a random Markov operator on a family of Schreier graphs of G associated with the action on a boundary of a binary rooted tree has a Cantor spectrum of the Lebesgue measure zero. This will be used to gain some information about the spectrum of the Cayley graph. The main tool of investigation is given by a substitution, that, on the one hand, gives a presentation of G in terms of generators and relations, and, on the other hand, defines a minimal substitutional dynamical system which leads to the use of the theory of random Shroedinger operator. No special knowledge is assumed, and the talk is supposed to be easily accessible for the audience.