##### Department of Mathematics,

University of California San Diego

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### Math 211B - Group Actions Seminar

## David Gao

#### UCSD

## Sofic actions on sets and applications to generalized wreath products

##### Abstract:

Inspired by the work of Hayes and Sale showing wreath products of two sofic groups are sofic, we define a notion of soficity for actions of countable discrete groups on countable discrete sets. We shall prove that, if the action $\alpha$ of G on X is sofic, G is sofic, and H is sofic, then the generalized wreath product H $\wr_\alpha$ G is sofic. We shall demonstrate several examples of sofic actions, including actions of sofic groups with locally finite stabilizers, all actions of amenable groups, and all actions of LERF groups. This talk is based on joint work with Srivatsav Kunnawalkam Elayavalli and Gregory Patchell.

Host: Brandon Seward

### March 14, 2024

### 10:00 AM

APM 7321

Research Areas

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