Speaker: Ayoub Hafid (the University of Tokyo)

Title: Concepts of coarse geometry on quantum metric spaces

Time/Date: April 21 (Tue), 2026, 4:45-6:15pm

Room: 126 Math. Sci. Building (It will be also online. The Zoom link is the same as before. If you don't have one, please ask Kawahigashi.)

Abstract: We present two different concepts of quantum metric spaces (quantum (noncommutative) versions of metric spaces), one based on Lipschitz seminorms (by Rieffel and Latremoliere) and the other based on quantum relations (by Kuperberg/ Weaver) and introduce a link between them. We then introduce examples of noncompact versions of these spaces and show how these allow us to talk about "structures at infinity", and to generalize concepts from coarse geometry and higher index theory. In particular we show how a higher index taking value in the K-groups of a Roe algebra can be constructed for locally compact metric spaces under some mild conditions on the commutators of their elements.