# Renormalization and Galois Theories

Share this page *Edited by *
*Alain Connes; Frédéric Fauvet; Jean-Pierre Ramis*

A publication of the European Mathematical Society

This volume is the outcome of a CIRM Workshop on Renormalization
and Galois Theories held in Luminy, France, in March 2006.
The subject of this workshop was the interaction and relationship
between four currently very active areas: renormalization in quantum
field theory (QFT), differential Galois theory, noncommutative
geometry, motives and Galois theory.

The last decade has seen a burst of new techniques to cope with
the various mathematical questions involved in QFT, with notably the
development of a Hopf-algebraic approach and insights into the
classes of numbers and special functions that systematically appear
in the calculations of perturbative QFT (pQFT). The analysis of
the ambiguities of resummation of the divergent series of pQFT,
an old problem, has been renewed, using recent results on Gevrey
asymptotics, generalized Borel summation, Stokes phenomenon
and resurgent functions.

The purpose of the present book is to highlight, in the context of
renormalization, the convergence of these various themes,
orchestrated by diverse Galois theories. It contains three lecture
courses together with five research articles and will be useful to both
researchers and graduate students in mathematics and physics.

A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and research mathematicians interested in renormalization and Galois Theories.