| Date: | October 9, 2020 |
| Time: | 11:00am |
| Location: | Zoom |
| Speaker: | James O'Quinn |
| Title: | Ergodic theorems and amenability |
| Abstract: | Ergodic theorems are one of the main technical cornerstones of ergodic
theory, which is the study of dynamical systems from a measurable
perspective. Roughly speaking, an ergodic theorem provides a relation
between averaging a function over the dynamics and and averaging a
function over the space for ergodic systems. Thinking of a dynamical
system as a group action on a measure space, the kind of averaging
necessary for ergodic theorems to hold happens readily for actions of
the integers, but may not be available for other groups. However,
amenable groups provide the type of averaging we need. During this
talk, I will introduce some of the main ideas in ergodic theory,
focusing on the ergodic theorems. I will also relate this to amenable
groups, which are objects of great interest in current research and
permeate many areas of analysis.
No background in dynamics or group theory is assumed for this talk.
Newcomers and those with a passing interest in this area are especially
encouraged to attend. |
|
| Date: | October 16, 2020 |
| Time: | 11:00am |
| Location: | Zoom |
| Speaker: | Alex Weygandt |
| Title: | Topological Dynamics and Operator Algebras |
| Abstract: | In topological dynamics, one studies (groups of) homeomorphisms on topological spaces. Under mild assumptions, one can generate C*-algebras, called transformation group C^*-algebras, which capture many of the properties of such dynamical systems. In this talk, I will define how one obtains transformation group C*-algebras, and discuss how properties of topological dynamical systems induce properties of the corresponding transformation group C*-algebra, and vice versa. |
|
| Date: | November 6, 2020 |
| Time: | 11:00am |
| Location: | Zoom |
| Speaker: | Konrad Wrobel |
| Title: | Cofinite equivariance and wreath products |
| Abstract: | We show all wreath products of cyclic groups with a given free group as the base space are orbit equivalent. In order to show this, we define the notion of a cofinitely equivariant and study how this property is preserved under free products. This is joint work with Robin Tucker-Drob. |
|
| Date: | November 20, 2020 |
| Time: | 11:00am |
| Location: | zoom |
| Speaker: | Josiah Owens |
| Title: | Schreier Graphs and Schreier Dynamical Systems: "Schreier! Graphin's!" -Gollum, the group theorist |
| Abstract: | The concept of a Schreier graph will be introduced as well as the space of Schreier graphs over a given finitely generated group and its topology. A dynamical system enacted by a group G on a space X (whether topological or measurable) can be isomorphically embedded into the space of Schreier graphs over G or the space of subgroups of G. A given Schreier graph can be associated with a (Schreier) dynamical system, described by its orbit in the space of Schreier graphs over G. We will show that if the action of G on X is minimal, then the orbit of a G-typical Schreier graph is dense in the isomorphic embedding of (G, X) in the space of Schreier graphs. |
|
Menu