##### Department of Mathematics,

University of California San Diego

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### Math 211B - Group Actions Seminar

## Qingyuan Chen

#### UCSD

## Shannon Orbit Equivalences Preserve Kolmogorov-Sinai Entropy

##### Abstract:

We will consider the behavior of the Kolmogorov-Sinai entropies of amenable group actions under a Shannon orbit equivalence. Although dynamical entropy is in general not invariant under orbit equivalences, recent works have shown that various notions of restricted orbit equivalences will preserve entropy. We focus on the case where the orbit equivalence is Shannon, and both groups are finitely generated amenable. In this talk, we will present a proof for our main result.

Host: Brandon Seward

### May 16, 2024

### 10:00 AM

APM 7321

Research Areas

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