Noncommutative geometry: metric and spectral aspects

Session

29-morning

29 Sept 2022, 09:00

12. Noncommutative spaces at finite resolution

Walter van Suijlekom

29/09/2022, 09:00

We extend the traditional framework of noncommutative geometry in order to deal with two types of approximation of metric spaces. On the one hand, we consider spectral truncations of geometric spaces, while on the other hand, we consider metric spaces up to a finite resolution. In our approach the traditional role played by C*-algebras is taken over by so-called operator systems. We consider...

11. Tolerance relations and quantization

Francesco D'Andrea

29/09/2022, 10:00

It is well known that “bad” quotient spaces can be studied by associating to them the groupoid C*-algebra of an equivalence relation. A similar procedure for relations that are reflexive and symmetric but fail to be transitive leads to a non associative algebra. I will discuss some of its properties based on a recent joint work with G. Landi and F. Lizzi.

14. Spectral metric and Einstein tensors.

Ludwik Dabrowski

29/09/2022, 11:20

We define bilinear functionals of vector fields and differential forms, the densities of which yield the metric and Einstein tensors on even-dimensional Riemannian manifolds. We generalise these concepts in non-commutative geometry and, in particular, we prove that for the conformally rescaled geometry of the noncommutative two-torus the Einstein functional vanishes.

17. Causality in noncommutative deformation spacetimes

Nicolas Franco

29/09/2022, 12:20

A notion of causality specific to noncommutative geometry was introduced in 2013 by Franco and Eckstein, leading at the same time to a notion of Lorentzian metric. This notion has been widely explored with regards to almost-commutative space-times. In this talk, we present a more difficult exploration concerning "truly" noncommutative spacetimes, i.e. deformation spacetimes as Moyal spacetime...