## EVENT DETAILS AND ABSTRACT

**Dynamical Systems Seminar**
**Title:** Stability of groups, dynamical systems, and characters

**Speaker:** Itamar Vigdorovich

**Speaker Info:** Weizmann Institute of Science

**Brief Description:**

**Special Note**:

**Abstract:**

I will discuss three seemingly unrelated topics:
1. Group Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of finite-dimensional characters?
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures? Is every almost orbit close to an orbit?
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. The talk is based on a joint work with Arie Levit.

**Date:** Tuesday, October 03, 2023

**Time:** 3:00pm

**Where:** Lunt 104

**Contact Person:** Prof. Bryna Kra

**Contact email:** kra@math.northwestern.edu

**Contact Phone:** 847-491-5567

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