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Noncommutative geometry: metric and spectral aspects

28–30 Sept 2022
Europe/Warsaw timezone

Session

28-morning

28 Sept 2022, 08:45

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  1. 1. Atiyah sequences of braided Lie algebras and their splittings
    Giovanni Landi
    28/09/2022, 09:00
  2. 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.

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  3. 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...

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  4. 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,...

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  5. 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.

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