##### Department of Mathematics,

University of California San Diego

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### Math 211 B00 - Group Actions Seminar

## Riley Thornton

#### UCLA

## Cayley Diagrams and Factors of IID Processes

##### Abstract:

A Cayley diagram is a labeling of a graph $G$ that encodes an action of a group which induces $G$. For instance, a $d$-edge coloring of a $d$-regular tree is a Cayley diagram for the group $(\mathbb{Z}/2\mathbb{Z})^{*d}$. In this talk, we will investigate when a Cayley graph $G=(\Gamma, E)$ admits an $\operatorname{Aut}(G)$-f.i.i.d. Cayley diagram and show that $\Gamma$-f.i.i.d. solutions to local labeling problems for such graphs lift to $\operatorname{Aut}(G)$-f.i.i.d. solutions.

Host: Brandon Seward

### October 7, 2021

### 12:00 PM

Zoom ID 967 4109 3409 (email an organizer for the password)

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