Noncommutative geometry: metric and spectral aspects

Session

28-afternoon

28 Sept 2022, 14:30

20. Localization and quantum observers in some Lie-algebra type noncommutative spacetimes.

Fedele Lizzi

28/09/2022, 14:30

I will discuss how the observers in a noncommutative spacetime need to be considered quantum objects as well, and discuss issues of localization of states for kappa-Minkowski spaces and some (angular type) variants of it.

5. Curvature for modules over spectral triples

Bram Mesland

28/09/2022, 15:30

In this talk we introduce the curvature of densely defined universal connections on Hilbert C*-modules relative to a spectral triple, obtaining a well-defined curvature operator. Algebraically, this curvature can be interpeted as the defect of the unbounded Kasparov product to commute with the operation of taking squares. The definition recovers the represented curvature of finitely generated...

6. The Gromov-Hausdorff distance in noncommutative geometry: convergence of quantum compact metric spaces and their modules

Frederic Latremoliere

28/09/2022, 16:30

Connes' Spectral triples have emerged as the preferred tool to encode geometric information over possibly noncommutative C*-algebras. We present, in two lectures, a distance on the space of metric spectral triples, which then enables us to formally discuss ideas such as approximations or perturbations of spectral triples, and opens the possibility to study the geometry of spaces of spectral...