On March 8-13, 2004, a meeting was organized at the Luminy CIRM (France) on arithmetic and differential Galois groups, reflecting the growing interactions between the two theories. The present volume contains the proceedings of this conference. It covers the following themes: moduli spaces (of curves, of coverings, of connexions), including the recent developments on modular towers; the arithmetic of coverings and of differential equations (fields of definition, descent theory); fundamental groups; the inverse problems and methods of deformation; and the algorithmic aspects of the theories, with explicit computations or realizations of Galois groups.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians interested in mechanization of proofs and logical operations.

Table of Contents

• M. Berkenbosch -- Algorithms and moduli spaces for differential equations
• M. Berkenbosch and M. van der Put -- Families of linear differential equations on the projective line
• P. Boalch -- Brief introduction to Painlevé VI
• A. Buium -- Correspondences, Fermat quotients, and uniformization
• J.-M. Couveignes -- Jacobiens, jacobiennes et stabilité numérique
• P. Débes -- An introduction to the modular tower program
• M. Dettweiler and S. Wewers -- Variation of parabolic cohomology and Poincaré duality
• M. D. Fried -- The main conjecture of modular towers and its higher rank generalization
• R. Liţcanu and L. Zapponi -- Properties of Lamé operators with finite monodromy
• S. Malek -- On the Riemann-Hilbert problem and stable vector bundles on the Riemann sphere
• B. H. Matzat -- Integral $p$-adic differential modules
• F. Pop -- Galois theory of Zariski prime divisors
• M. Romagny and S. Wewers -- Hurwitz spaces
• D. Semmen -- The group theory behind modular towers
• C. Simpson -- Formalized proof, computation, and the construction problem in algebraic geometry
• Annexe. Liste des participants