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# Résultats de recherche

**3322**

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## Jérémie Szeftel The resolution of the bounded L2 curvature conjecture in General Relativity (Part 2)

In order to control locally a space-‐time which satisfies the Einstein equations, what are the minimal assumptions one should make on its curvature tensor? The bounded L2 curvature conjecture roughly asserts that one should only need L2 bounds of the curvature tensor on a given space-‐like hypersurface. This conjecture has its roots in the remarkable developments of the last twenty years centered around the issue of optimal well-‐posedness for nonlinear wave equations. In this context, a corresponding conjecture for nonlinear wave equations cannot hold, unless the nonlinearity has a very special nonlinear structure. I will present the proof of this ... Voir la vidéole (1h57m42s)

## Jérémie Szeftel The resolution of the bounded L2 curvature conjecture in General Relativity (Part 1)

In order to control locally a space time which satisfies the Einstein equations, what are the minimal assumptions one should make on its curvature tensor? The bounded L2 ... Voir la vidéole (55m20s)

## Jérémie Szeftel - General relativity (Workshop)

In order to control locally a space time which satisfies the Einstein equations, what are the minimal assumptions one should make on its curvature tensor? The bounded L2 ... Voir la vidéole (2h9m13s)

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

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 ... Voir la vidéole (2h7m51s)

## Andras Vasy - Microlocal analysis and wave propagation (Part 2)

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!) ... Voir la vidéole (2h12m10s)

## Andras Vasy - Microlocal analysis and wave propagation (Part 3)

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!) ... Voir la vidéole (2h8m16s)

## Andras Vasy - Microlocal analysis and wave propagation (Part 4)

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!) ... Voir la vidéole (0s)

## Andras Vasy - Quasilinear waves and trapping: Kerr‐de Sitter space

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 ... Voir la vidéole (1h5s)