indisponible
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

indisponible
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

indisponible
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, dynamics, institut fourier, number theory, summer school

indisponible
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, dynamics, institut fourier, summer school, number theory

We will first introduce the basic concepts pertaining to Kobayashi pseudo-distances and hyperbolic complex spaces, including Brody’s theorem and the Ahlfors-Schwarz lemma. One of the main goals of the theory is to understand conditions under which a given algebraic variety is Kobayashi hyperbolic. This leads to the introduction of jet spaces and jet metrics, and provides a strong link between the existence of entire curves and the existence of global algebraic differential equations.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, COURBES PSEUDOHOLOMORPHES

We will first introduce the basic concepts pertaining to Kobayashi pseudo-distances and hyperbolic complex spaces, including Brody’s theorem and the Ahlfors-Schwarz lemma. One of the main goals of the theory is to understand conditions under which a given algebraic variety is Kobayashi hyperbolic. This leads to the introduction of jet spaces and jet metrics, and provides a strong link between the existence of entire curves and the existence of global algebraic differential equations.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES

We will first introduce the basic concepts pertaining to Kobayashi pseudo-distances and hyperbolic complex spaces, including Brody’s theorem and the Ahlfors-Schwarz lemma. One of the main goals of the theory is to understand conditions under which a given algebraic variety is Kobayashi hyperbolic. This leads to the introduction of jet spaces and jet metrics, and provides a strong link between the existence of entire curves and the existence of global algebraic differential equations.  
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES

We will first introduce the basic concepts pertaining to Kobayashi pseudo-distances and hyperbolic complex spaces, including Brody’s theorem and the Ahlfors-Schwarz lemma. One of the main goals of the theory is to understand conditions under which a given algebraic variety is Kobayashi hyperbolic. This leads to the introduction of jet spaces and jet metrics, and provides a strong link between the existence of entire curves and the existence of global algebraic differential equations.  
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES

The study of the asymptotic behavior of higher spin fields has proven to be a key point in understanding the stability properties of the Einstein equations. Penrose derived in the 60s the asymptotic behavior of these higher spin fields from a representation by Hertz potentiels satisfying a wave equation and a decay Ansatz for the solutions of the wave equation. The purpose of this talk is to perform the construction by Penrose in the context of the Cauchy problem on Minkowski space -­time for Maxwell fields and linearized gravity. Considering a Cauchy problem for Maxwell fields and linearized gravity with data in weighted Sobolev spaces, a Hertz potential is build from a generalization of the de Rham complex to arbitrary spin. The asymptotic behavior of these higher spin fields is then derived from the asymptotic behavior of the solutions of the wave equation.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis

In order to control locally a space time which satisfies the Einstein equations, what are the minimal assumptions one should make on its curvature tensor? The bounded L2 curvature conjecture roughly asserts that one should only need L2 bounds of the curvature tensor on a given space like hypersurface. This conjecture has its roots in the remarkable developments of the last twenty years centered around the issue of optimal well posedness for nonlinear wave equations. In this context, a corresponding conjecture for nonlinear wave equations cannot hold, unless the nonlinearity has a very special nonlinear structure. I will present the proof of this conjecture, which sheds light on the specific null structure of the Einstein equations. This is joint work with Sergiu Klainerman and Igor Rodnianski.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis