Model Theory and an Ocneanu Ultraproduct for General Von Neumann Algebras

Abstract: The model theories of tracial von Neumann algebras and, more recently, sigma-finite von Neumann algebras have led to a large body of work and applications in operator algebras. I will discuss recent work removing the sigma-finiteness condition, yielding a completely general model theory of von Neumann algebras. After reviewing existing ultraproduct constructions in von Neumann algebras, I will introduce and characterize the ultraproduct corresponding to this new framework and show how it generalizes important properties of the Ocneanu ultraproduct. I will also discuss potential future work. Partially joint work with Goldbring, Hart, and Sinclair.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | slides )

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Noncommutative geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click meet.google.com/zjd-ehrs-wtx (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.

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