20 décembre 2017

Yang Liu (IHES et Max-Planck Institut (Bonn))
Hypergeometric function and modular curvature

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Lieu : Institut de Mathématique d'Orsay (IMO) Salle 0A3

Résumé : In the recent development of modular geometry on toric noncommutative manifolds, metrics are parametrized by self-adjoint elements in the coordinate algebra (noncommutative in general), whose exponential are called Weyl factors. Local invariants, such as the Riemannian curvature are encoded in the coefficients of heat kernel expansion of some Laplacian type operator. The inner automorphisms generated by the Weyl factors induces a derivation (a noncommutative differential) at the infinitesimal. From analytic point of view, curvature is designed to measure the commutators of covariant derivatives. Therefore in the noncommutative setting, the modular curvature has a quantum part coming from the interplay between the inner automorphisms and the classical differentials. In this talk, I will report a recent progress that the spectral functions that define the action of inner automorphisms are sums of hypergeometric functions and their multivariable generalization.

Hypergeometric function and modular curvature  Version PDF