École Doctorale Mathématiques et STIC

Mathematical Problems in General Relativity - Pr Richard Schoen

Professeur Richard SCHOEN, Stanford University

Institut Henri Poincaré 11 rue Pierre & Marie Curie - 75005 Paris - (Accès)

Dates du module : 28, 29 novembre 2011 et 5, 6 décembre 2011.

Catégorie : CS - Cours Scientifiques de niveau doctoral

Domaine : Mathématiques

Durée : 14 heures

Programme :

This course will introduce the Einstein equations and describe some mathematical problems which arise in their study. We will focus on areas in which recent progress has been made. Topics will include the Cauchy problem and the constraint equations. We will describe questions concerning the asymptotic behavior of solutions of the constraint equations and density theorems. These will elucidate the behavior of the energy and linear and angular momentum for asymptotically flat spacetime. We will describe recent progress on mass/angular momentum inequalities. We will also discuss questions relating to gravitational energy and positive energy theorems as well as notions of quasilocal mass. Some of the tools here include minimal hypersurface theory, inverse mean curvature flow, and the Dirac operator.

Prérequis : Géométrie Riemannienne de base, en particulier géométrie des sous variétés. Analyse fonctionnelle classique espaces de Sobolev et de Hölder. Équations elliptiques sur les variétés.