##### Department of Mathematics,

University of California San Diego

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### Math 211B - Group Actions Seminar

## Robin Tucker-Drob

#### University of Florida

## Amenable subrelations of treed equivalence relations and the Paddle-ball lemma

##### Abstract:

We give a comprehensive structural analysis of amenable subrelations of a treed quasi-measure preserving equivalence relation. The main philosophy is to understand the behavior of the Radon-Nikodym cocycle in terms of the geometry of the amenable subrelation within the tree. This allows us to extend structural results that were previously only known in the measure-preserving setting, e.g., we show that every nowhere smooth amenable subrelation is contained in a unique maximal amenable subrelation. The two main ingredients are an extension of Carrière and Ghys's criterion for nonamenability, along with a new Ping-Pong-style argument we call the "Paddle-ball lemma" that we use to apply this criterion in our setting. This is joint work with Anush Tserunyan.

Host: Brandon Seward

### May 19, 2022

### 10:00 AM

AP&M 6402

Zoom ID 967 4109 3409

Email an organizer for the password

Research Areas

Ergodic Theory and Dynamical Systems****************************