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Date
Editeur
Auteur
Titre
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Andras Vasy - Microlocal analysis and wave propagation (Part 3)
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
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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Andras Vasy - Microlocal analysis and wave propagation (Part 2)
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
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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Andras Vasy - Microlocal analysis and wave propagation (Part 1)
/ Fanny Bastien
/ 16-06-2014
/ Canal-u.fr
Vasy Andràs
Voir le résumé
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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Amortissement Landau - Cédric Villani
/ Société Française de Physique
/ 05-07-2011
/ Canal-U - OAI Archive
Société Française de Physique
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Voir le résumé
Congrès Général de la SFP Bordeaux-2011 mardi 5 juillet 2011Amortissement Landau Cédric VILLANI, Institut Camillle-Jordan, Lyon, et Institut Henri-Poincaré, Paris Médaille Fields de mathématiques 2010 Mot(s) clés libre(s) : Landau, mathématiques
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algos de maths: programmer des calculs numériques et géométriques
/ INRIA, Unisciel, Fuscia, Université de Nice
/ 2011
/ Unisciel
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Voir le résumé
Permet de réaliser toutes les activités d'initiation à l'algorithmique en mathématiques. Un grand nombre de contenus et sujets sont disponibles (manipuler des tableaux, faire des tris numériques, manipuler le hasard, ..). Mot(s) clés libre(s) : proglet, algorithmique en mathématiques, algorithmes pour les maths
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Alexandre Sukhov - J-complex curves: some applications (Part 4)
/ Fanny Bastien
/ 28-06-2012
/ Canal-u.fr
Sukhov Alexandre
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Voir le résumé
We
will focus in our lectures on the following : 1. J-complex discs in
almost complex manifolds : general properties. Linearization and
compactness. Gromov’s method : the Fredholm alternative for the d-bar
operator. Attaching a complex disc to a Lagrangian manifold.
Application : exotic symplectic structures. Hulls of totally real
manifolds : Alexander’s theorem. 2. Real surfaces in (almost) complex
surfaces. Filling real 2-spheres by a Levi-flat hypersurface (Bedford
-Gaveau-Gromov theorem). Some applications. Symplectic and contact
structures. Reeb foliation and the Weinsten conjecture. Hofer’s proof of
the Weinstein conjecture. 3. J-complex lines and hyperbolicity. The KAM
theory and Moser’s stability theorem for entire J-complex curves in
tori. Global deformation and Bangert’s theorem. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
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Alexandre Sukhov - J-complex curves: some applications (Part 3)
/ Fanny Bastien
/ 27-06-2012
/ Canal-u.fr
Sukhov Alexandre
Voir le résumé
Voir le résumé
We
will focus in our lectures on the following : 1. J-complex discs in
almost complex manifolds : general properties. Linearization and
compactness. Gromov’s method : the Fredholm alternative for the d-bar
operator. Attaching a complex disc to a Lagrangian manifold.
Application : exotic symplectic structures. Hulls of totally real
manifolds : Alexander’s theorem. 2. Real surfaces in (almost) complex
surfaces. Filling real 2-spheres by a Levi-flat hypersurface (Bedford
-Gaveau-Gromov theorem). Some applications. Symplectic and contact
structures. Reeb foliation and the Weinsten conjecture. Hofer’s proof of
the Weinstein conjecture. 3. J-complex lines and hyperbolicity. The KAM
theory and Moser’s stability theorem for entire J-complex curves in
tori. Global deformation and Bangert’s theorem. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
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Alexander Strohmaier - Workshop
/ Fanny Bastien
/ 03-07-2014
/ Canal-u.fr
Strohmaier Alexander
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Voir le résumé
I will explain how one can formulate and formalize the Gupta Bleuler framework for the Quantization of the electromagnetic field in an algebraic manner so that it works on globally hyperbolic space times. I will then discuss a construction of physical representations that works without the "spectral gap assumption" in the case of absense of zero energy resonances. These can be excluded by topologocial restrictions at infinity. This is based on joint work with Felix Finster. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
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Alexander Gorodnik - Diophantine approximation and flows on homogeneous spaces (Part 3)
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
Voir le résumé
The
fundamental problem in the theory of Diophantine approximation is to
understand how well points in the Euclidean space can be approximated by
rational vectors with given bounds on denominators. It turns out that
Diophantine properties of points can be encoded using flows on
homogeneous spaces, and in this course we explain how to use techniques
from the theory of dynamical systems to address some of questions in
Diophantine approximation. In particular, we give a dynamical proof of
Khinchin’s theorem and discuss Sprindzuk’s question regarding
Diophantine approximation with dependent quantities, which was solved
using non-divergence properties of unipotent flows. In conclusion we
explore the problem of Diophantine approximation on more general
algebraic varieties. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, dynamics, institut fourier, summer school, number theory
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Alexander Gorodnik - Diophantine approximation and flows on homogeneous spaces (Part 2)
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
Voir le résumé
The
fundamental problem in the theory of Diophantine approximation is to
understand how well points in the Euclidean space can be approximated by
rational vectors with given bounds on denominators. It turns out that
Diophantine properties of points can be encoded using flows on
homogeneous spaces, and in this course we explain how to use techniques
from the theory of dynamical systems to address some of questions in
Diophantine approximation. In particular, we give a dynamical proof of
Khinchin’s theorem and discuss Sprindzuk’s question regarding
Diophantine approximation with dependent quantities, which was solved
using non-divergence properties of unipotent flows. In conclusion we
explore the problem of Diophantine approximation on more general
algebraic varieties. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, dynamics, institut fourier, summer school, number theory
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Accéder à la ressource
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