##### Department of Mathematics,

University of California San Diego

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### Math 243 - Functional Analysis Seminar

## Pieter Spaas

#### UCSD

## Non-classification of Cartan subalgebras for a class of von Neumann algebras

##### Abstract:

We study the complexity of the classification problem for Cartan subalgebras in von Neumann algebras. We will discuss a construction that leads to a family of II$_1$ factors whose Cartan subalgebras, up to unitary conjugacy, are not classifiable by countable structures. We do this via establishing a strong dichotomy, depending if the action is strongly ergodic or not, on the complexity of the space of homomorphisms from a given equivalence relation to $E_0$. We will start with some of the necessary preliminaries, and then outline the proofs of the aforementioned results.

Host: Adrian Ioana

### November 27, 2017

### 12:00 PM

### AP&M 6402

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