In noncommutative geometry, an essential question is to extend the notion of metric and curvature in Riemannian geometry to noncommutative spaces in a operator theoretical framework. A fundamental feature, in contrast to Riemannian geometry, is the fact that metrics are parametrized by noncommutative coordinates. In the conformal geometry of noncommutative tori, the new structure in the modular analog of the Gaussian curvature consists of two spectral functions, which compress the ansatz caused by the noncommutativity between the metric coordinate and its derivatives. In the first part of the talk, I will explain the higher dimensional generalization of a fantastic functional equation between them due to Connes and Moscovici. In the second part, I will show that hypergeometric functions are the build blocks of those spectral functions. A surprising discovery, obtained by combining the power of hypergeometric functions and computer algebra systems, is that ConnesMoscovici functional relation can be extended to a continuous family with respect to the dimension parameter.
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Modular curvature and Hypergeometric functions
Research Group:
Yang Liu
Institution:
Max Planck (Bonn)
Location:
A136
Schedule:
Monday, April 16, 2018  14:00 to 15:00
Abstract:
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Upcoming events

Yash Jhaveri
On the (in)stability of the identity map in optimal transportation
Tuesday, April 24, 2018  14:30

Mikhail Sychev
Lower semicontinuity and relaxation for extendedvalued integrands
Tuesday, April 24, 2018  16:00

Christopher J. Larsen
Minimality for limits of unilateral cohesive energy minimizers
Thursday, April 26, 2018  16:00

Riccardo Montalto
Normal form coordinates for the KdV equation near finite gap potentials
Thursday, May 3, 2018  14:30
Today's Lectures

Antonio Lerario
09:00 to 11:00

Luca Heltai
11:00 to 13:00

Gianluigi Rozza
11:00 to 13:00

Fabio Cavalletti
11:00 to 13:00

Ugo Boscain
11:00 to 13:00
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A. Michelangeli; P.Thanh Nam; A. Olgiati,Ground state energy of mixture...

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