Time: 20.4.2021 at 13:00
Speaker: Ville Salo, University of Turku
Title: Self-simulable groups
Abstract: We say a group G simulates a subgroup H < G if every effective H-system on the Cantor set can be realized as a dynamical factor of the H-subaction of a tiling system on G. A theorem of Hochman shows that Z^3 simulates Z, and a theorem of Durand-Romashenko-Shen/Aubrun-Sablik shows that Z^2 simulates every effective subshift on Z. It is open whether any group simulates itself, but it is known that any such must be group is non-amenable and one-ended. We give the first examples of such self-simulable groups. The examples include almost all braid groups, [outer] automorphism groups of free groups, general linear groups over integers, Brin-Thompson groups nV, Burger-Mozes lattices, many right-angled Artin groups, and non-amenable branch groups. For almost all of these groups this also gives the first examples of strongly aperiodic tiling systems. In the talk, we give the necessary background, outline how self-simulation is obtained for the square of any non-abelian free group, and explain how to get the more interesting examples using closure properties.