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Date
Editeur
Auteur
Titre
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Andras Vasy - Microlocal analysis and wave propagation (Part 1)
/ Fanny Bastien
/ 16-06-2014
/ Canal-u.fr
Vasy Andràs
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Voir le résumé
In these lectures I will explain the basics of microlocal analysis, emphasizing non elliptic problems, such as wave propagation, both on manifolds without boundary, and on manifolds with boundary. In the latter case there is no `standard' algebra of differential, or pseudodifferential, operators; I will discuss two important frameworks: Melrose's totally characteristic, or b, operators and scattering operators. Apart from the algebraic and mapping properties, I will discuss microlocal ellipticity, real principal type propagation, radial points and generalizations, as well as normally hyperbolic trapping. The applications discussed will include Fredholm frameworks (which are thus global even for non elliptic problems!) for the Laplacian on asymptotically hyperbolic spaces and the wave operator on asymptotically de Sitter spaces, scattering theory for `scattering metrics' (such as the `large ends' of cones), wave propagation on asymptotically Minkowski spaces and generalizations (`Lorentzian scattering metrics') and on Kerr de Sitter type spaces. The lectures concentrate on linear PDE, but time permitting I will briefly discuss nonlinear versions. The lecture by the speaker in the final workshop will use these results to solve quasilinear wave equations globally, including describing the asymptotic behavior of solutions, on Kerr de Sitter spaces. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
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Compter les triangles
/ Inria / Interstices
/ 09-09-2020
/
Trystram Denis
Voir le résumé
Voir le résumé
Certains comptent les moutons pour s’endormir, les citadins que nous sommes devenus sont aujourd’hui réduits à compter autre chose... comme des triangles par exemple. Découvrez comment l’étude d’un jeu peut faire aborder quelques règles fondamentales de dénombrement. Mot(s) clés libre(s) : dénombrement, énumération, triangles
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Emmanuel Trélat - Théorie du contrôle optimal et applications aux missions spatiales
/ Fanny Bastien
/ 11-02-2016
/ Canal-u.fr
Trélat Emmanuel
Voir le résumé
Voir le résumé
La problématique du contrôle optimal est de guider l'évolution en temps
d'un système donné vers une configuration finale souhaitée, tout en
minimisant un certain critère. Le point saillant de cette théorie, qui
généralise le calcul des variations, est le principe du maximum de
Pontryagin, qui donne des conditions nécessaires d'optimalité du premier
ordre. Du point de vue numérique ce principe réduit le problème initial
à un problème aux deux bouts qui peut être résolu par une méthode de
tir.
En pratique il est très difficile de faire converger numériquement une
méthode de tir, et elle doit être combinée à d'autres approches. Je
parlerai ici, sur des exemples motivés par l'aérospatiale, des méthodes
de continuation numérique, de contrôle géométrique, puis d'éléments de
théorie des systèmes dynamiques qui, convenablement utilisés, permettent
de planifier des missions spatiales interplanétaires. Mot(s) clés libre(s) : théorie du contrôle, Grenoble (Isère), institut fourier, colloquium mathalp, aérospatial
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Tatiana Toro - Geometry of measures and applications (Part 5)
/ Fanny Bastien
/ 19-06-2015
/ Canal-u.fr
Toro Tatiana
Voir le résumé
Voir le résumé
In the 1920's Besicovitch studied
linearly measurable sets in the plane, that is sets with locally finite
"length". The basic question he addressed was whether the infinitesimal
properties of the "length" of a set E in the plane yield geometric
information on E itself. This simple question marks the beginning of the
study of the geometry of measures and the associated field known as
Geometric Measure Theory (GMT).
In
this series of lectures we will present some of the main results in the
area concerning the regularity of the support of a measure in terms of
the behavior of its density or in terms of its tangent structure. We
will discuss applications to PDEs, free boundary regularity problem and
harmonic analysis. The aim is that the GMT component of the mini-course
will be self contained. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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Tatiana Toro - Geometry of measures and applications (Part 4)
/ Fanny Bastien
/ 18-06-2015
/ Canal-u.fr
Toro Tatiana
Voir le résumé
Voir le résumé
In the 1920's Besicovitch studied
linearly measurable sets in the plane, that is sets with locally finite
"length". The basic question he addressed was whether the infinitesimal
properties of the "length" of a set E in the plane yield geometric
information on E itself. This simple question marks the beginning of the
study of the geometry of measures and the associated field known as
Geometric Measure Theory (GMT).
In
this series of lectures we will present some of the main results in the
area concerning the regularity of the support of a measure in terms of
the behavior of its density or in terms of its tangent structure. We
will discuss applications to PDEs, free boundary regularity problem and
harmonic analysis. The aim is that the GMT component of the mini-course
will be self contained. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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Tatiana Toro - Geometry of measures and applications (Part 3)
/ Fanny Bastien
/ 17-06-2015
/ Canal-u.fr
Toro Tatiana
Voir le résumé
Voir le résumé
In the 1920's Besicovitch studied
linearly measurable sets in the plane, that is sets with locally finite
"length". The basic question he addressed was whether the infinitesimal
properties of the "length" of a set E in the plane yield geometric
information on E itself. This simple question marks the beginning of the
study of the geometry of measures and the associated field known as
Geometric Measure Theory (GMT).
In
this series of lectures we will present some of the main results in the
area concerning the regularity of the support of a measure in terms of
the behavior of its density or in terms of its tangent structure. We
will discuss applications to PDEs, free boundary regularity problem and
harmonic analysis. The aim is that the GMT component of the mini-course
will be self contained. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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Tatiana Toro - Geometry of measures and applications (Part 2)
/ Fanny Bastien
/ 16-06-2015
/ Canal-u.fr
Toro Tatiana
Voir le résumé
Voir le résumé
In the 1920's Besicovitch studied
linearly measurable sets in the plane, that is sets with locally finite
"length". The basic question he addressed was whether the infinitesimal
properties of the "length" of a set E in the plane yield geometric
information on E itself. This simple question marks the beginning of the
study of the geometry of measures and the associated field known as
Geometric Measure Theory (GMT).
In
this series of lectures we will present some of the main results in the
area concerning the regularity of the support of a measure in terms of
the behavior of its density or in terms of its tangent structure. We
will discuss applications to PDEs, free boundary regularity problem and
harmonic analysis. The aim is that the GMT component of the mini-course
will be self contained. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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Accéder à la ressource
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Tatiana Toro - Geometry of measures and applications (Part 1)
/ Fanny Bastien
/ 16-06-2015
/ Canal-u.fr
Toro Tatiana
Voir le résumé
Voir le résumé
In the 1920's Besicovitch studied
linearly measurable sets in the plane, that is sets with locally finite
"length". The basic question he addressed was whether the infinitesimal
properties of the "length" of a set E in the plane yield geometric
information on E itself. This simple question marks the beginning of the
study of the geometry of measures and the associated field known as
Geometric Measure Theory (GMT).
In
this series of lectures we will present some of the main results in the
area concerning the regularity of the support of a measure in terms of
the behavior of its density or in terms of its tangent structure. We
will discuss applications to PDEs, free boundary regularity problem and
harmonic analysis. The aim is that the GMT component of the mini-course
will be self contained. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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Accéder à la ressource
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Yoshihiro Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 5)
/ Fanny Bastien
/ 18-06-2015
/ Canal-u.fr
Tonegawa Yoshihiro
Voir le résumé
Voir le résumé
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
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Yoshihiro Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 4)
/ Fanny Bastien
/ 17-06-2015
/ Canal-u.fr
Tonegawa Yoshihiro
Voir le résumé
Voir le résumé
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
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Accéder à la ressource
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