Quantised differential calculus and Hilbert transform

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• Paul Meunier, ENS Lyon
• Friday 26 November 2021, 16:00-17:00
• MR11.

If you have a question about this talk, please contact Macarena Arenas.

In his journey into the noncommutative world of operators on the separable Hilbert space, Alain Connes encountered a new differential calculus, generalising the classical (commutative) case on manifolds. I will present the definition of quantised differential calculus, and give an example on the real line R. Surprisingly, there is a canonical choice of such a calculus which corresponds to a very classical tool, the Hilbert transform, a well-known operator in signal processing and real analysis.

This talk is part of the Junior Geometry Seminar series.

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