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Nombre de programmes trouvés : 800
Cours magistraux

le (1h24m41s)

Tropp 8/9 - Random matrix theory and computational linear algebra

This course treats some contemporary algorithms from computational linear algebra that involve random matrices. Rather than surveying the entire field, we focus on a few algorithms that are both simple and practically useful. We begin with an introduction to matrix concentration inequalities, which are a powerful tool for analyzing structured random matrices. We use these ideas to study matrix approximations constructed via randomized sampling, such as the random features method. As a more sophisticated application, we present a complete treatment of a recent algorithm for solving graph Laplacian linear systems in near-linear time. Some references : 1. Tropp, "An introduction to ...
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Cours magistraux

le (1h25m5s)

Gilles Courtois - The Margulis lemma, old and new (Part 2)

The Margulis lemma describes the structure of the group generated by small loops in the fundamental group of a Riemannian manifold, thus giving a picture of its local topology. Originally stated for homogeneous spaces by C. Jordan, L. Bieberbach, H. J. Zassenhaus, D. Kazhdan-G. Margulis, it has been extended to the Riemannian setting by G. Margulis for manifolds of non positive curvature. The goal of these lectures is to present the recent work of  V. Kapovitch and B. Wilking who gave a sharp version of the Margulis lemma under the assumption that the Ricci curvature is bounded below. Their method ...
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Cours magistraux

le (1h25m8s)

Feng Luo - An introduction to discrete conformal geometry of polyhedral surfaces (Part 5)

The goal of the course is to introduce some of the recent developments on discrete conformal geometry of polyhedral surfaces. We plan to cover the following topics.- The Andreev-Koebe-Thurston theorem on circle packing polyhedral metrics and Marden-Rodin’s proof- Thurston’s conjecture on the convergence of circle packings to the Riemann mapping and its solution by Rodin-Sullivan- Finite dimensional variational principles associated to polyhedral surfaces- A discrete conformal equivalence of polyhedral surfaces and its relationship to convex polyhedra in hyperbolic 3-space- A discrete uniformization theorem for compact polyhedral surfaces- Convergence of discrete conformality and some open problems
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Cours magistraux

le (1h25m27s)

Yoshihiro Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 5)

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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