Title: A Tour of Rigidity in Ergodic Theory
Speaker: Kelly B. Yancey (Institute for Defense Analyses)
Webpage: https://www.kellybyancey.com
Abstract:
A dynamical system can be thought of as a probability space equipped with a self map that is invariant with respect to the measure. In the field of ergodic theory one of the things that we study is the long term behavior of such dynamical systems. In this talk I will begin with some basic constructions in ergodic theory and explain how the study began. I will then move on to describe a generic class of maps called rank-one transformations and a method to construct them. We will discuss the rigidity property of dynamical systems and explore the partial rigidity of Chacon's transformation, a classic map that was the first example of a map that is weakly mixing but not strongly mixing.
With these examples under our belt, I will describe some new results by Jon Fickenscher and myself on characterizing rank-one rigid maps. For rank-one systems we will examine partial rigidity and bound the partial rigidity constant away from one for a subclass of transformations that are canonically bounded (a term coined by Gao and Hill). We will also discuss rigidity in the unbounded case.
