Noncommutative geometry: metric and spectral aspects

Session

28-morning

28 Sept 2022, 08:45

1. Atiyah sequences of braided Lie algebras and their splittings

Giovanni Landi

28/09/2022, 09:00

2. Dual of the dual formula for the distance in noncommutative geometry

Pierre Martinetti

28/09/2022, 10:00

Connes's spectral distance is an extended metric on the state space of a C*-algebra, generalizing Kantorovich's dual formula of the Wasserstein distance of order 1 from optimal transport. It is expressed as a supremum. We present a dua formula - as an infimum - generalizing Beckmann's ``dual of the dual'' formulation of the Wasserstein distance.

7. Spectral gaps for higher Laplacians and group cohomology

Piotr Mizerka

28/09/2022, 11:20

I will focus on the cohomology of finitely presented groups. I plan to investigate two conditions concerning it: vanishing and reducibility (for all unitary representations). These conditions are related to Kazhdan's property (T): vanishing and reducibility coincide in degree one and are equivalent to this property. It is already known, due to the work of Dymara and Januszkiewicz, that this...

24. Spectral triple with real structure on fuzzy sphere

Anwesha Chakraborty

28/09/2022, 11:45

Here we have illustrated the construction of a real structure on a fuzzy sphere S^*_2 in its spin-1/2 representation. Considering the SU(2) covariant Dirac and chirality operator on S^∗_2 given by U. C. Watamura et.al. [Commun. Math. Phys. 183, 365–382 (1997)], we have shown that the real structure is consistent with other spectral data for KO dimension-4 fulfilling the zero order condition,...

25. Hopf algebroids on quantum projective spaces

Jacopo Zanchettin

28/09/2022, 12:10

We construct the Ehresmann-Schauenburg bialgebroid for a family of U(1)-quantum principal bundles over quantum projective spaces, showing that another antipode (related to K-theory on the base algebra) exists besides the "classical" flip. Moreover, we show how the theory of twists (generalized characters) applies in this situation.