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Cours magistraux

le (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 ...
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Cours magistraux

le (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 ...
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Cours magistraux

le (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 ...
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Cours magistraux

le (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 ...
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Cours magistraux

le (2h4m52s)

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 vidéo