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Nombre de programmes trouvés : 1624
Cours magistraux

le (1h55m11s)

Dominique Cerveau - Holomorphic foliations of codimension one, elementary theory (Part 3)

In this introductory course I will present the basic notions, both local and global, using classical examples. I will explain statements in connection with the resolution of singularities with for instance the singular Frobenius Theorem or the Liouvilian integration. I will also present some open questions which I will motivate by examples. Dans ce cours introductif je m’attacherai à présenter les notions de base tant locales que globales au travers d’exemples classiques. J’aborderai des énoncés liés à la résolution des singularités avec par ...
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Cours magistraux

le (1h55m24s)

Yoshihiro Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 1)

The course covers two separate but closely related topics. The first topic is the mean curvature flow in the framework of GMT due to Brakke. It is a flow of varifold moving by the generalized mean curvature. Starting from a quick review on the necessary tools and facts from GMT and the definition of the Brakke mean curvature flow, I will give an overview on the proof of the local regularity theorem. The second topic is the reaction-diffusion approximation of phase boundaries with key words such as the Modica-Mortola functional and ...
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Cours magistraux

le (1h55m56s)

Lars Andersson - Geometry and analysis in black hole spacetimes (Part 4)

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 ...
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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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