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Nombre de programmes trouvés : 929
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 (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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