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An Isaac Newton Institute Workshop

Trends in Noncommutative Geometry

QG and RH, an analogy.

18th December 2006

Author: alain connes (College de France)

Abstract

We shall start from the role of KMS states in two different contexts, first in arithmetic then in the electroweak phase transition in particle physics. We shall then build a dictionary between the set-up of noncommutative geometry leading to the spectral realization of the zeros of the Riemann zeta function and a tentative set-up to encode the spectral model in Lorentzian signature, allowing to relate to cosmological models. This is joint work with Matilde Marcolli.