Geometric and differential Galois theories

On March 29-April 2, 2010, a meeting was organized at the Luminy CIRM (France) on geometric and differential Galois theories, witnessing the close ties these theories have woven in recent years. The present volume collects the Proceedings of this meeting. Although it may be viewed as a continuation of the one held 6 years earlier on arithmetic and differential Galois groups (see Séminaires et Congrès, vol. 13), several new and promising themes have appeared. The articles gathered here cover the following topics : moduli spaces of connexions, differential equations and coverings in finite characteristic, liftings, monodromy groups in their various guises (tempered fundamental group, motivic groups, generalized difference Galois groups), and arithmetic applications.