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: