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

Michele Cirafici
A survey of the GMN construction
Friday, February 21, 2020  12:00

Giuliano Klun
Periodic solutions of nearly integrable Hamiltonian systems bifurcating from infinitedimensional tori
Friday, February 21, 2020  14:00

Andreas Bernig
Algebraic Integral Geometry
Monday, February 24, 2020  16:00

Susanna Terracini
The nodal set of solutions to sublinear, discontinuous and singular equations
Tuesday, February 25, 2020  11:00
Today's Lectures

09:00 to 11:00

09:15 to 11:15

11:00 to 13:00

13:30 to 16:30
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