# Sieye Ryu (BGU): Predictability and Entropy for Actions of Amenable Groups and Non-amenable Groups

Suppose that a countable group $G$ acts on a compact metric space $X$ and that $S \subset G$ is a semigroup not containing the identity of $G$. If every continuous function $f$ on $X$ is contained in the closed algebra generated by $\{sf : s \in S\}$, the action is said to be $S$-predictable. In this talk, we consider the following question due to Hochman: When $G$ is amenable, does $S$-predictability imply zero topological entropy? To provide an affirmative answer, we introduce the notion of a random invariant order. If time permits, we will explain how the answer extends to non-amenable groups using recent results of Seward on Rokhlin entropy. This is a joint work with Tom Meyerovitch.

## Date:

Tue, 26/06/2018 - 14:15 to 15:15