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Caltech

Logic Seminar

Tuesday, November 28, 2017
3:00pm to 4:00pm
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Building 15, Room 131
Non-classification of Cartan subalgebras for a class of von Neumann algebras
Pieter Spaas, Department of Mathematics, UCSD,
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.
For more information, please contact Mathematics Department by phone at 626-395-4335 or by email at [email protected].