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# Résultats de recherche

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## Lars Andersson - Symmetry operators and energies

Black holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity.Following a brief introduction to the evolution problem for theEinstein equations, I will give some background on geometry of the Kerr spacetime. Theanalysis of fields on the exterior of the Kerr black hole serve as important model problems for the black hole stability problem. I will discuss some of the difficulties one encounters in analyzing waves in ... Voir la vidéole (1h55m38s)

## Rod Gover - An introduction to conformal geometry and tractor calculus (Part 1)

After recalling some features (and the value of) the invariant ``Ricci calculus'' of pseudo-‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal ... Voir la vidéole (2h4m58s)

## Rod Gover - An introduction to conformal geometry and tractor calculus (Part 2)

After recalling some features (and the value of) the invariant ``Ricci calculus'' of pseudo-‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal covariance is visited and some covariant/invariant equations from physics are recovered in this framework. Motivated by the need to develop a more effective approach to such problems we are led into the idea of conformal geometry and a conformally invariant calculus; this``tractor calculus'' is then developed explicitly. We will discuss how to calculate using this, and touch on applications to the construction of conformal invariants and conformally invariant differential operators. The second ... Voir la vidéole (1h58m33s)

## Rod Gover - An introduction to conformal geometry and tractor calculus (Part 3)

After recalling some features (and the value of) the invariant ``Ricci calculus'' of pseudo-‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal covariance is visited and some covariant/invariant equations from physics are recovered in this framework. Motivated by the need to develop a more effective approach to such problems we are led into the idea of conformal geometry and a conformally invariant calculus; this``tractor calculus'' is then developed explicitly. We will discuss how to calculate using this, and touch on applications to the construction of conformal invariants and conformally invariant differential operators. The second ... Voir la vidéole (1h56m12s)

## Rod Gover - An introduction to conformal geometry and tractor calculus (Part 4)

After recalling some features (and the value of) the invariant ``Ricci calculus'' of pseudo-‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal covariance is visited and some covariant/invariant equations from physics are recovered in this framework. Motivated by the need to develop a more effective approach to such problems we are led into the idea of conformal geometry and a conformally invariant calculus; this``tractor calculus'' is then developed explicitly. We will discuss how to calculate using this, and touch on applications to the construction of conformal invariants and conformally invariant differential operators. The second ... Voir la vidéole (1h1m56s)

## Rod Gover - Geometric Compactification, Cartan holonomy, and asymptotics

Conformal compactification has long been recognised as an effective geometric framework for relating conformal geometry, and associated field theories ``at infinity'', to the asymptotic phenomena of an interior ... Voir la vidéole (1h55m53s)

## Jérémie Szeftel The resolution of the bounded L2 curvature conjecture in General Relativity (Part 4)

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 (1h56m15s)

## Jérémie Szeftel The resolution of the bounded L2 curvature conjecture in General Relativity (Part 3)

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 (2h4m52s)