Gianluca Basso
Gianluca Basso: The universal minimal flow of topological groups beyond Polish
11/06/20 22:59
Tuesday, June 16, 2020 17:15
Location: Zoom.us: if you want to participate please contact organizers
Speaker: Gianluca Basso (Université de Lausanne & Torino)
Title: The universal minimal flow of topological groups beyond Polish
Abstract. When \(G\) is a Polish group, one way of knowing that it has "nice" dynamics is to show that \(M(G)\), the universal minimal flow of \(G\), is metrizable. For non-Polish groups, this is not the relevant dividing line: the universal minimal flow of \( \mathrm{Sym}(\kappa) \) is the space of linear orders on \(\kappa\)—not a metrizable space, but still "nice"—, for example. In this talk, we present a set of equivalent properties of topological groups which characterize having "nice" dynamics. We show that the class of groups satisfying such properties is closed under some topological operations and use this to compute the universal minimal flows of some concrete groups, like \(\mathrm{Homeo}(\omega_{1})\). This is joint work with Andy Zucker.
Location: Zoom.us: if you want to participate please contact organizers
Speaker: Gianluca Basso (Université de Lausanne & Torino)
Title: The universal minimal flow of topological groups beyond Polish
Abstract. When \(G\) is a Polish group, one way of knowing that it has "nice" dynamics is to show that \(M(G)\), the universal minimal flow of \(G\), is metrizable. For non-Polish groups, this is not the relevant dividing line: the universal minimal flow of \( \mathrm{Sym}(\kappa) \) is the space of linear orders on \(\kappa\)—not a metrizable space, but still "nice"—, for example. In this talk, we present a set of equivalent properties of topological groups which characterize having "nice" dynamics. We show that the class of groups satisfying such properties is closed under some topological operations and use this to compute the universal minimal flows of some concrete groups, like \(\mathrm{Homeo}(\omega_{1})\). This is joint work with Andy Zucker.