Tracial metric geometry

Bhishan Jacelon (Institute of Mathematics CAS)

Thursday 8th October 15:00-16:00
Maths 311B

Abstract

My recent work pairs optimal transport theory together with classification theory, with the goal of developing the metric geometry of suitable embedding spaces (or more precisely, spaces of approximate unitary equivalence classes of unital *-monomorphisms). In this talk, I will focus on commutative domains C(X), and monotracial codomains like the Jiang-Su algebra or a II_1 factor. In this setting, we will see how to adapt the classical Hoffman--Wielandt theorem, which computes the 2-norm unitary orbit distance between normal operators as the 2-Wasserstein distance between spectral measures. I will also describe a noncommutative replacement Z(X) of C(X) whose associated tracial geometry is particularly appealing.

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