Logic Seminar

Todor TsankovUniversity of Lyon
Topological dynamics of kaleidoscopic groups

Friday, February 4, 2022 - 2:45pm
Zoom

Kaleidoscopic groups are infinite permutation groups recently introduced by Duchesne, Monod, and Wesolek by analogy with a classical construction of Burger and Mozes of subgroups of automorphism groups of regular trees. In contrast with the Burger-Mozes groups, kaleidoscopic groups are never locally compact and they are realized as subgroups of the homeomorphism groups of Wazewski dendrites (tree-like, compact spaces whose branch points are dense). The input for the construction is a finite or infinite permutation group Gamma and the output is the kaleidoscopic group $K(\Gamma)$.

In this talk, I will discuss recent joint work with Gianluca Basso, in which we characterize the metrizability of the universal minimal flow of $K(\Gamma)$ in terms of the original group $\Gamma$. This generalizes previous work of Duchesne and Kwiatkowska who have calculated the universal minimal flows for some special $\Gamma$.