Séminaires et Congrès 2007; 391 pp; softcover Number: 13 ISBN10: 2856292224 ISBN13: 9782856292228 List Price: US$110 Member Price: US$88 Order Code: SECO/13
 On March 813, 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 RiemannHilbert 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
