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Last update: 23/03/2003

 Houches March 2003

École de physique des Houches

A Connes
Galoisian symmetries and renormalization


Abstract:

The aim of the class is to account for two dual topics where physics and number theory are deeply intertwined. The first is my joint work with Kreimer on renormalization and the Riemann Hilbert problem. The latter is the corner stone of differentiable Galois theory and the first aim will be to understand the renormalization group under this light, in relation with the Galois theory at Archimedian places. The second is the spectral analysis of the Adele class space as a natural "compactification" of the central object GL(n,Q)\GL(n,A) of the Langlands program, and its relation for n=2 with the Hopf algebra of codimension 1 transverse geometry.

lecture: