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Séminaire de Mathématique

Hypergeometric function and modular curvature

by Prof. Yang Liu (Max Planck Institute for Mathematics, Bonn & IHES)

lundi 18 décembre 2017 de au (Europe/Paris)
at IHES ( Amphithéâtre Léon Motchane )
Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
Description

In the recent development of modular geometry on toric noncommutative manifolds (Connes-Moscovici 2014), metrics are parametrized by self-adjoint elements in the ambient C*-algebra, whose exponential are called Weyl factors. Local invariants, such as the Riemannian curvature, are encoded in the coefficients of certain heat kernel expansion. The new ingredient, purely due to noncommutativity, is the the inner automorphism generated by the Weyl factor, whose corresponding derivation can be viewed as a noncommutative differential.  From analytic point of view, curvature is designed to measure the commutators of covariant derivatives. In this talk, we will discuss some intriguing spectral functions which define the interplay between the inner automorphisms and the classical differentials.  I recently found that hypergeometric functions and its multivariable generalization are the building blocks. Geometric applications such as Gauss-Bonnet theorem lead to some functional relations/equations between them which are still begging for more conceptual understanding.

Organisé par Maxim Kontsevich
Contact Email: cecile@ihes.fr