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Andras Vasy - Microlocal analysis and wave propagation (Part 1) (en Anglais)


URL d'accès : http://www.canal-u.tv/?redirectVideo=22531...

Droits : CC BY-NC-ND 4.0

Auteur(s) : Vasy Andràs, Bastien Fanny
16-06-2014

Description : 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.
Mots-clés libres : mathématiques,Grenoble,école d'été,General Relativity,institut fourier,summer school,asymptotic analysis
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Type : image en mouvement
Format : video/x-flv


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rtmpt://fms2.cerimes.fr:80/vod/institut_fourier/andras.vasy.microlocal.analysis.and.wave.propagation.part.1._22531/vasy_ecoleete_16062014_sd.mp4


Entrepôt d'origine : Canal-u.fr
Identifiant : oai:canal-u.fr:22531
Type de ressource : Ressource documentaire
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Ressource pédagogique

Andras Vasy - Microlocal analysis and wave propagation (Part 1) (en Anglais)


URL d'accès : http://www.canal-u.tv/video/institut_fourier/andra...
rtmpt://fms2.cerimes.fr:80/vod/institut_fourier/an...

Identifiant de la fiche : 22531
Schéma de la métadonnée : LOMv1.0, LOMFRv1.0

Droits : libre de droits, gratuit
Droits réservés à l'éditeur et aux auteurs. CC BY-NC-ND 4.0

Auteur(s) : VASY ANDRÀS
Éditeur(s) : Fanny Bastien
16-06-2014

Description : 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.
Mots-clés libres : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis

Classification UNIT : Mathématiques > Fondamentaux
Classification : Mathématiques et Sciences de la nature et de la matière > Mathématiques
Indice(s) Dewey: Mathématiques (510)


PEDAGOGIQUE

Type pédagogique : cours / présentation

Niveau : doctorat



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Type de contenu : image en mouvement
Format : video/x-flv
Taille : 4.68 Go
Durée d'exécution : 2 heures 9 minutes 13 secondes



RELATIONS


Cette ressource fait partie de :
  • Ecoles d'été
  • 2014



Entrepôt d'origine : Canal-u.fr
Identifiant : oai:canal-u.fr:22531
Type de ressource : Ressource pédagogique
Exporter au format XML