##### Department of Mathematics,

University of California San Diego

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### Math 243 - Functional Analysis Seminar

## Pieter Spaas

#### UCLA

## Furstenberg-Zimmer structure theory for actions on von Neumann algebras

##### Abstract:

In classical ergodic theory, compact and weakly mixing actions/extensions have been well-studied. The main structural result from Furstenberg and Zimmer states that every action can be written as "a weakly mixing extension of a tower of compact extensions". We will discuss some of these classical results and their motivation, and consider similar notions for actions on von Neumann algebras which have been defined throughout the years. We will then complete (part of) the picture by establishing equivalence of several such notions, followed by some consequences and open questions. This is partially based on joint work with Asgar Jamneshan.

Host: Adrian Ioana

### April 19, 2022

### 11:00 AM

APM 7218 and Zoom

Email djekel@ucsd.edu for Zoom info

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