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Mots-clefs > S > summer school
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  • 140 ressources ont été trouvées. Voici les résultats 11 à 20
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Karma Dajani - An introduction to Ergodic Theory of Numbers (Part 3)

/ Fanny Bastien / Canal-u.fr
Voir le résumé
Voir le résumé
In this course we give an introduction to the ergodic theory behind common number expansions, like expansions to integer and non-integer bases, Luroth series and continued fraction expansion. Starting with basic ideas in ergodic theory such as ergodicity, the ergodic theorem and natural extensions, we apply these to the familiar expansions mentioned above in order to understand the structure and global behaviour of different number theoretic expansions, and to obtain new and old results in an elegant and straightforward manner.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, dynamics, institut fourier, summer school, number theory
 |  Accéder à la ressource

Jérémie Szeftel The resolution of the bounded L2 curvature conjecture in General Relativity (Part 3)

/ Fanny Bastien / Canal-u.fr
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Voir le résumé
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. These lectures will start from scratch and require no specific background.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
 |  Accéder à la ressource

Jérémie Szeftel The resolution of the bounded L2 curvature conjecture in General Relativity (Part 2)

/ Fanny Bastien / Canal-u.fr
Voir le résumé
Voir le résumé
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. These lectures will start from scratch and require no specific background.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
 |  Accéder à la ressource

Jean-Pierre Demailly - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties (Part 4)

/ Fanny Bastien / Canal-u.fr
Voir le résumé
Voir le résumé
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
 |  Accéder à la ressource

Jean-Pierre Demailly - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties (Part 3)

/ Fanny Bastien / Canal-u.fr
Voir le résumé
Voir le résumé
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
 |  Accéder à la ressource

Jean-Pierre Demailly - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties (Part 2)

/ Fanny Bastien / Canal-u.fr
Voir le résumé
Voir le résumé
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
 |  Accéder à la ressource

Jean-Louis Verger-Gaugry - Limit Equidistribution (Part 2)

/ Fanny Bastien / Canal-u.fr
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Voir le résumé
indisponible
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, dynamics, institut fourier, summer school, number theory
 |  Accéder à la ressource

Guy David - Minimal sets (Part 2)

/ Fanny Bastien / Canal-u.fr
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Voir le résumé
indisponible
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
 |  Accéder à la ressource

Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 3)

/ Fanny Bastien / Canal-u.fr
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Voir le résumé
In these lectures I will first recall the basic notions and results that are needed to study minimal surfaces in the smooth setting (above all the area formula and the first variation of the area), give a short review of the main (classical) techniques for existence results, and then outline the theory of Finite Perimeter Sets, including the main results of the theory (compactness, structure of distributional derivative, rectifiability). If time allows, I will conclude with a few applications.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
 |  Accéder à la ressource

Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 2)

/ Fanny Bastien / Canal-u.fr
Voir le résumé
Voir le résumé
In these lectures I will first recall the basic notions and results that are needed to study minimal surfaces in the smooth setting (above all the area formula and the first variation of the area), give a short review of the main (classical) techniques for existence results, and then outline the theory of Finite Perimeter Sets, including the main results of the theory (compactness, structure of distributional derivative, rectifiability). If time allows, I will conclude with a few applications.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
 |  Accéder à la ressource

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