A note to readers: This book is in French.

As in the preceding volumes of this seminar, at which more than one thousand talks have been presented, this volume includes sixteen survey lectures on topics of current interest: three lectures on analysis and geometry, three about algebraic geometry, three on diophantine geometry, two related to Langlands' program, two about group theory, one on algebraic topology, one related to Ising's model, and two about mathematical physics.

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 analysis, geometry, Langlands' program, mathematical physics, and Ising's model.

Table of Contents

• O. Glass -- La méthode du retour en contrôlabilité et ses applications en mécanique des fluides
• E. Kowalski -- Crible en expansion
• H. Miller -- Kervaire invariant one
• W. Werner -- Analyticité discrète du modèle d'Ising

• C. Breuil -- Correspondance de Langlands \(p\)-adique, compatibilité local-global et applications
• A. Chambert-Loir -- Relations de dépendance et intersections exceptionnelles
• A. Naor -- Sparse quadratic forms and their geometric applications
• F. Santambrogio -- Inégalités isopérimétriques quantitatives via le transport optimal

• T. C. Hales -- The fundamental lemma and the Hitchin fibration
• A. Oancea -- Invariants de Welschinger
• T. Scanlon -- A proof of the André-Oort conjecture via mathematical logic
• C. Voisin -- Sections rationnelles de fibrations sur les surfaces et conjecture de Serre

• C. Houdayer -- Invariant percolation and measured theory of nonamenable groups
• D. Huybrechts -- A global Torelli theorem for hyperkähler manifolds
• P. Mironescu -- Le déterminant jacobien
• F. Planchon -- Existence globale et scattering pour les solutions de masse finie de l'équation de Schrödinger cubique en dimension deux
• Table par noms d'auteurs