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

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Development of Reduced Order CFD models with ITHACAFV for a nuclear physics application
Wednesday, October 17, 2018  14:00

Carlo Scarpa
An introduction to complex manifolds
Wednesday, October 17, 2018  16:30

Giovanni Bellettini
Apparent contours and reconstruction of solid shapes
Thursday, October 18, 2018  16:00

Monica Nonino
Reduced order methods for fluid structure interaction problems and reduction of the Kolmogorov nwidth
Friday, October 19, 2018  14:00
Today's Lectures

Guido De Philippis
10:00 to 13:00

Don Zagier (ICTP)
11:00 to 13:00

Antonio Lerario
11:00 to 13:00

Antonio Lerario, Fabio Cavalletti
13:30 to 15:00
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