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Mots-clefs > I > institut fourier
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  • 156 ressources ont été trouvées. Voici les résultats 1 à 10
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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
 |  Accéder à la ressource

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
 |  Accéder à la ressource

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
 |  Accéder à la ressource

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
 |  Accéder à la ressource

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
 |  Accéder à la ressource

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
 |  Accéder à la ressource

Bernard Parisse - GIAC/XCAS and PARI/GP

/ Fanny Bastien / Canal-u.fr
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indisponible
Mot(s) clés libre(s) : colloques, mathématique, Grenoble (Isère), institut fourier
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Bill Allombert - New GP features

/ Fanny Bastien / Canal-u.fr
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pas disponible
Mot(s) clés libre(s) : mathématiques, colloques, Grenoble (Isère), institut fourier
 |  Accéder à la ressource

Bruno Lévy - A numerical algorithm for L2 semi-discrete optimal transport in 3D

/ Fanny Bastien / Canal-u.fr
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indisponible
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
 |  Accéder à la ressource

Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 1)

/ Fanny Bastien / Canal-u.fr
Voir le résumé
Voir le résumé
A celebrated theorem of Almgren shows that every integer rectifiable current which minimizes (locally) the area is a smooth submanifold except for a singular set of codimension at most 2. Almgren’s theorem is sharp in codimension higher than 1, because holomorphic subvarieties of Cn are area-minimizing. In fact the typical singularity of a 2-dimensional area-minimizing current is modelled by branch points of holomorphic curves. These singularities are rather difficult to analyze because they might be very high order phenomena.
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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