# Category: Memphis Graduate Seminar

# Generalizations of Alladi’s formula for arithmetical semigroups

# On the classification of generalized Baumslag-Solitar groups

Abstract: A generalized Baumslag-Solitar group (GBS group) is a group that acts on a tree with infinite cyclic edge and vertex stabilizers. Equivalently, it is the fundamental group of a graph of infinite cyclic groups. These groups have arisen in the study of splitting of groups. In this talk, we will discuss how to approach the group-theoretic classification of GBS groups and the current results of this problem.

# A theorem by Peres and Schlag

Abstract: In this talk, we will prove that if is lacunary, i.e. for every , then we can find an irrational number such that

# Basics of Abstract Harmonic Analysis

Speaker: Conner Griffin

Location: DH 313

Time: 3:00PM Fri. 3/25/2022

Abstract: Abstract harmonic analysis is an attractive theory that draws on many areas of mathematics. This talk will be an overview of some of the basics of harmonic analysis on locally compact abelian groups. It will lead into the definition of the Fourier transform for functions defined on such groups.

# Invariant ergodic measure, Mean dimension, and the small boundary property

Time: Fri 2/25 3:00 PM

Speaker: Xin Ma

Location: Dunn Hall 313

Title: Invariant ergodic measure, Mean dimension, and the small boundary property.

Abstract: In topological dynamics, the mean dimension can be used to classify dynamical systems. The small boundary property, related to mean dimension zero, was introduced by Weiss and Lindenstrauss, which is also found to have something to do with the structure theory of C*-algebras recently. In this talk, we mainly discuss the relationships among the three concepts in the title and see some applications. I will start from the very beginning of the topics. No specific background is assumed.