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Auteur
Titre
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Maciej Zworski - From redshift effect to classical dynamics : microlocal proof of Smale's conjecture
/ Fanny Bastien
/ 30-06-2014
/ Canal-u.fr
Zworski Maciej
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Voir le résumé
Dynamical zeta functions of Selberg, Smale and Ruelle are analogous to the Riemann zeta function with the product over primes replaced by products over closed orbits of Anosov flows. In 1967 Smale conjectured that these zeta functions should be meromorphic but admitted "that a positive answer would be a little shocking". Nevertheless the continuation was proved in 2012 by Giulietti-Liverani-Pollicott. By combining the Faure Sjöstrand approach to Anosov flows and Melrose's microlocal radial estimates, Dyatlov and I gave a simple proof of that conjecture. The same radial estimates were used by Vasy to provide a microlocal explanation of the redshift effect and propagation estimates for Kerr de Sitter like spaces. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
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Neshan Wickramasereka - Stability in minimal and CMC hypersurfaces
/ Fanny Bastien
/ 30-06-2015
/ Canal-u.fr
Wickramasereka Neshan
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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
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Claude Viterbo - Théorie des faisceaux et Topologie symplectique (Part 1)
/ Fanny Bastien
/ 03-07-2012
/ Canal-u.fr
Viterbo Claude
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Voir le résumé
L’utilisation
de méthodes de théorie des faisceaux (Kashiwara-Schapira)a été
dévelopée ces dernières années par Tamarkin, Nadler, Zaslow, Guillermou,
Kashiwara et Schapira. Nous essaierons d’en donner un aperçu à la fois
pour démontrer des résultats classiques, comme la conjecture d’Arnold,
et pour des résultats nouveaux.
The
use of methods from the Sheaf Theory (Kashiwara-Schapira) was
developped recently by Tamarkin, Nadler, Zaslow, Guillermou, Kashiwara
and Schapira. We will try to give an insight of that, in order to prove
classical results, such as the Arnold conjecture, and to obtain new
results.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
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Jean-Louis Verger-Gaugry - Limit Equidistribution (Part 1)
/ Fanny Bastien
/ 26-06-2013
/ Canal-u.fr
Verger-Gaugry Jean-Louis
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Voir le résumé
indisponible Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, dynamics, institut fourier, number theory, summer school
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Andras Vasy - Quasilinear waves and trapping: Kerr‐de Sitter space
/ Fanny Bastien
/ 30-06-2014
/ Canal-u.fr
Vasy Andràs
Voir le résumé
Voir le résumé
In this talk I will describe recent work with Peter Hintz on globally solving quasilinear wave equations in the presence of trapped rays, on Kerr de Sitter space, and obtaining the asymptotic behavior of solutions. For the associated linear problem without trapping, one would consider a global, non elliptic, Fredholm framework; in the presence of trapping the same framework is available for spaces of growing functions only. In order to solve the quasilinear problem we thus combine these frameworks with the normally hyperbolic trapping results of Dyatlov and a Nash Moser iteration scheme. 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
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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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Tatiana Toro - Geometry of measures and applications (Part 5)
/ Fanny Bastien
/ 19-06-2015
/ Canal-u.fr
Toro Tatiana
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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
|
Accéder à la ressource
|
|
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