Tri :
Date
Editeur
Auteur
Titre
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Bruno Lévy - A numerical algorithm for L2 semi-discrete optimal transport in 3D
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
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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Bill Allombert - New GP features
/ Fanny Bastien
/ Canal-u.fr
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Voir le résumé
pas disponible Mot(s) clés libre(s) : mathématiques, colloques, Grenoble (Isère), institut fourier
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Bernard Parisse - GIAC/XCAS and PARI/GP
/ Fanny Bastien
/ Canal-u.fr
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Voir le résumé
indisponible Mot(s) clés libre(s) : colloques, mathématique, Grenoble (Isère), institut fourier
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Andrew Lorent - The Aviles-Giga functional: past and present
/ Fanny Bastien
/ Canal-u.fr
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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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Andras Vasy - Microlocal analysis and wave propagation (Part 4)
/ 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 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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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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Maciej Zworski - From redshift effect to classical dynamics : microlocal proof of Smale's conjecture
/ Fanny Bastien
/ 30-06-2014
/ Canal-u.fr
Zworski Maciej
Voir le résumé
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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