##### Department of Mathematics,

University of California San Diego

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### Math 211 - Group Actions Seminar

## Gianluca Basso - Postdoctoral Scholar

#### Universit\'{e} Claude Bernard Lyon 1

## Topological dynamics beyond Polish groups

##### 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 the symmetric group of a set of cardinality $\kappa$ 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.

Host: Brandon Seward

### February 23, 2021

### 9:00 AM

### Zoom ID 967 4109 3409 (email Nattalie Tamam or Brandon Seward for the password)

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