Noncommutative geometry: metric and spectral aspects

Session

29-afternoon

Sep 29, 2022, 2:30 PM

15. Lorentzian spectral zeta functions

Michał Wrochna

9/29/22, 2:30 PM

The spectral theory of the Laplace–Beltrami operator on Riemannian manifolds is known to be intimately related to geometric invariants such as the Einstein-Hilbert action. These relationships have inspired many developments in physics including the Chamseddine–Connes action principle in the non-commutative geometry programme. However, a priori they do only apply to the case of Euclidean...

16. Quantum metric structures on q-deformed spaces

David Kyed

9/29/22, 3:30 PM

I will survey recent results concerning the quantum metric structures on the Podleś sphere and quantum SU(2). Along the way, I will provide a brief introduction to Rieffel’s theory of compact quantum metric spaces and the notion of quantum Gromov-Hausdorff convergence. The talk is based on joint works with Konrad Aguilar, Thomas Gotfredsen and Jens Kaad.

13. The Gromov-Hausdorff distance in noncommutative geometry: convergence of spectral triples

Frederic Latremoliere

9/29/22, 4:30 PM

We present a distance on the class of metric spectral triples. It thus becomes possible to formally discuss the idea of approximating a spectral triple with others: for instance, to approximate a spectral triple on the 2-torus by means of natural spectral triples on the finite dimensional so-called fuzzy tori.

A spectral triple induces an extended pseudo-metric on the state space of its...