In these lectures, Gromov{Witten theory will be introduced, assuming only basic moduli theory covered in the rst week of the School. Then the Crepant Transformation Conjecture will be explained. Some examples, with emphasis on the projective/global cases, will be given. Note: The construction of virtual fundamental class, which forms the foundation of the GW theory, will be given in Jun Li's concurrent lectures and will not be explained here.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, courbes, institut fourier, summer school, Gromov-Witten

In these lectures, Gromov{Witten theory will be introduced, assuming only basic moduli theory covered in the rst week of the School. Then the Crepant Transformation Conjecture will be explained. Some examples, with emphasis on the projective/global cases, will be given. Note: The construction of virtual fundamental class, which forms the foundation of the GW theory, will be given in Jun Li's concurrent lectures and will not be explained here.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, courbes, institut fourier, summer school, Gromov-Witten

The course covers two separate but closely related topics. The first topic is the mean curvature flow in the framework of GMT due to Brakke. It is a flow of varifold moving by the generalized mean curvature. Starting from a quick review on the necessary tools and facts from GMT and the definition of the Brakke mean curvature flow, I will give an overview on the proof of the local regularity theorem. The second topic is the reaction-diffusion approximation of phase boundaries with key words such as the Modica-Mortola functional and the Allen-Cahn equation. Their singular perturbation problems are related to objects such as minimal surfaces and mean curvature flows in the framework of GMT.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

The course covers two separate but closely related topics. The first topic is the mean curvature flow in the framework of GMT due to Brakke. It is a flow of varifold moving by the generalized mean curvature. Starting from a quick review on the necessary tools and facts from GMT and the definition of the Brakke mean curvature flow, I will give an overview on the proof of the local regularity theorem. The second topic is the reaction-diffusion approximation of phase boundaries with key words such as the Modica-Mortola functional and the Allen-Cahn equation. Their singular perturbation problems are related to objects such as minimal surfaces and mean curvature flows in the framework of GMT.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

The course covers two separate but closely related topics. The first topic is the mean curvature flow in the framework of GMT due to Brakke. It is a flow of varifold moving by the generalized mean curvature. Starting from a quick review on the necessary tools and facts from GMT and the definition of the Brakke mean curvature flow, I will give an overview on the proof of the local regularity theorem. The second topic is the reaction-diffusion approximation of phase boundaries with key words such as the Modica-Mortola functional and the Allen-Cahn equation. Their singular perturbation problems are related to objects such as minimal surfaces and mean curvature flows in the framework of GMT.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

The course covers two separate but closely related topics. The first topic is the mean curvature flow in the framework of GMT due to Brakke. It is a flow of varifold moving by the generalized mean curvature. Starting from a quick review on the necessary tools and facts from GMT and the definition of the Brakke mean curvature flow, I will give an overview on the proof of the local regularity theorem. The second topic is the reaction-diffusion approximation of phase boundaries with key words such as the Modica-Mortola functional and the Allen-Cahn equation. Their singular perturbation problems are related to objects such as minimal surfaces and mean curvature flows in the framework of GMT.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

The course covers two separate but closely related topics. The first topic is the mean curvature flow in the framework of GMT due to Brakke. It is a flow of varifold moving by the generalized mean curvature. Starting from a quick review on the necessary tools and facts from GMT and the definition of the Brakke mean curvature flow, I will give an overview on the proof of the local regularity theorem. The second topic is the reaction-diffusion approximation of phase boundaries with key words such as the Modica-Mortola functional and the Allen-Cahn equation. Their singular perturbation problems are related to objects such as minimal surfaces and mean curvature flows in the framework of GMT.
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

Le but de cet exposé est de présenter des généralisations multidimensionnelles des fractions continues et de l’algorithme d’Euclide d’un point de vue systèmes dynamiques, en nous concentrant sur les liens avec la numération et les substitutions. Nous allons considérer principalement deux types de généralisations, à savoir, les algorithmes définis par homographies, comme l’algorithme de Jacobi-Perron, et les fractions continues associées aux algorithmes de réduction dans les réseaux.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, dynamics, institut fourier, summer school, number theory

Le but de cet exposé est de présenter des généralisations multidimensionnelles des fractions continues et de l’algorithme d’Euclide d’un point de vue systèmes dynamiques, en nous concentrant sur les liens avec la numération et les substitutions. Nous allons considérer principalement deux types de généralisations, à savoir, les algorithmes définis par homographies, comme l’algorithme de Jacobi-Perron, et les fractions continues associées aux algorithmes de réduction dans les réseaux.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, dynamics, institut fourier, summer school, number theory