##### Department of Mathematics,

University of California San Diego

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### Math 211B - Group Actions Seminar

## Sebastián Barbieri

#### Universidad de Santiago de Chile

## Self-simulable groups

##### Abstract:

We say that a finitely generated group is self-simulable if every action of the group on a zero-dimensional space which is effectively closed (this means it can be described by a Turing machine in a specific way) is the topological factor of a subshift of finite type on said group. Even though this seems like a property which is very hard to satisfy, we will show that these groups do exist and that their class is stable under commensurability and quasi-isometries of finitely presented groups. We shall present several examples of well-known groups which are self-simulable, such as Thompson's V and higher-dimensional general linear groups. We shall also show that Thompson's group F satisfies the property if and only if it is non-amenable, therefore giving a computability characterization of this well-known open problem. Joint work with Mathieu Sablik and Ville Salo.

Host: Brandon Seward

### January 27, 2022

### 12:00 PM

Zoom ID 967 4109 3409

Email an organizer for the password

Research Areas

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