A quantization of coarse structures and uniform Roe algebras

David Sherman (University of Virginia)

29-Apr-2022, 19:00-20:00 (23 months ago)

Abstract: A coarse structure is a way of talking about "large-scale" properties. It is encoded in a family of relations that often, but not always, come from a metric. A coarse structure naturally gives rise to Hilbert space operators that in turn generate a so-called uniform Roe algebra.

In ongoing work with Bruno Braga and Joe Eisner, we use ideas of Weaver to construct "quantum" coarse structures and uniform Roe algebras in which the underlying set is replaced with an arbitrary represented von Neumann algebra. The general theory immediately applies to quantum metrics (suitably defined), but it is much richer. We explain another source of examples based on measure instead of metric, leading to a large and easy-to-understand class of new C*-algebras.

I will present the big picture: where uniform Roe algebras come from, how Weaver's framework facilitates our definitions. I will focus on a few illustrative examples and will not assume any familiarity with coarse structures or von Neumann algebras.

mathematical physicsanalysis of PDEsclassical analysis and ODEscategory theorycomplex variablesfunctional analysislogicmetric geometryoptimization and control

Audience: researchers in the topic


VCU ALPS (Analysis, Logic, and Physics Seminar)

Series comments: Description: Research seminar on topics ranging from analysis and logic to mathematical physics.

Meetings will be conducted over Zoom:

Meeting ID: 951 0562 0974

The password is 10 characters, consisting of the name of the ancient Greek mathematician who wrote "Elements" (first letter capitalized) followed by the first 4 primes.

Organizer: Ihsan Topaloglu*
Curators: Marco Aldi*, Brent Cody, Sean D. Cox, Alex Misiats, Allison Moore*
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