title: Self-simulable groups.
Abstract: We say that a finitely generated group is self-simulable if every action on a zero-dimensional space which is effectively closed (this means it is “computable” 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 satisfy nice stability properties. We shall present several examples of these groups, including a proof that Thompson’s group F satisfies the property if and only if it is non-amenable. Joint work with Mathieu Sablik and Ville Salo.