##### Department of Mathematics,

University of California San Diego

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### Math 211 B00 - Group Actions Seminar

## Anton Bernshteyn

#### Georgia Tech

## Equivariant maps to free and almost free subshifts

##### Abstract:

Let $\Gamma$ be a countably infinite group. Seward and Tucker-Drob proved that every free Borel action of $\Gamma$ on a Polish space $X$ admits a Borel equivariant map $\pi$ to the free part of the Bernoulli shift $k^\Gamma$, for any $k \geq 2$. Our goal in this talk is to generalize this result by putting extra restrictions on the image of $\pi$. For instance, can we ensure that $\pi(x)$ is a proper coloring of the Cayley graph of $\Gamma$ for all $x \in X$? More generally, can we guarantee that the image of $\pi$ is contained in a given subshift of finite type? The main result of this talk is a positive answer to this question in a very broad (and, in some sense, optimal) setting. The main tool used in the proof of our result is a probabilistic technique for constructing continuous functions with desirable properties, namely a continuous version of the Lov\'{a}sz Local Lemma.

Host: Brandon Seward

### October 14, 2021

### 12:00 PM

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

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