Logic Seminar

Andy Zucker University of Lyon
Topological dynamics beyond Polish groups

Tuesday, May 5, 2020 - 2:55pm
Zoom

When $G$ is a Polish group, one way of knowing that $G$ has "nice" dynamics is to show that $M(G)$, the universal minimal flow of $G$, is metrizable. However, works of Bartosova, Gheysens, and Krupinski--Pillay investigate groups beyond the Polish realm, such as $Sym(\kappa)$, $Homeo(\omega_1)$, and automorphism groups of uncountable, $\omega$-homogeneous structures. For example, Bartosova shows that the universal minimal flow of $Sym(\kappa)$ is the space of linear orders on $\kappa$--not a metrizable space, but still "nice." In this talk, we seek to put these results into a general framework which encompasses all topological groups.

This is joint work with Gianluca Basso