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Documents  Pajot, Hervé | enregistrements trouvés : 9

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Research talks;Combinatorics;Topology

The Toeplitz square peg problem asks if every simple closed curve in the plane inscribes a square. This is known for sufficiently regular curves (e.g. polygons), but is open in general. We show that the answer is affirmative if the curve consists of two Lipschitz graphs of constant less than 1 using an integration by parts technique, and give some related problems which look more tractable.

55N45

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Outreach;Mathematics Education and Popularization of Mathematics

Terence Tao (born 17 July 1975) is an Australian-American mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory. As of 2015, he holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. Tao was a co-recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics. Terence Tao (born 17 July 1975) is an Australian-American mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory. As of 2015, he holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. Tao was a ...

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- x; 306 p.
ISBN 978-1-107-68949-7

London mathematical society lecture note series , 0413

Localisation : Collection 1er étage

analyse combinatoire # matrice # transport optimal # flot de Ricci # équation de Euler # inégalité fonctionnelle # condition de courbure-dimension # embouteillage

00B25 ; 49-06 ; 53-06 ; 90-06 ; 91-06 ; 35-06 ; 28-06 ; 60-06 ; 65-06 ; 37-06 ; 76-06 ; 82-06

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Research talks;Partial Differential Equations

In a joint work with Maria Colombo and Luigi De Rosa we consider the Cauchy problem for the ipodissipative Navier-Stokes equations, where the classical Laplacian $-\Delta$ is substited by a fractional Laplacian $(-\Delta)^\alpha$. Although a classical Hopf approach via a Galerkin approximation shows that there is enough compactness to construct global weak solutions satisfying the energy inequality à la Leray, we show that such solutions are not unique when $\alpha$ is small enough and the initial data are not regular. Our proof is a simple adapation of the methods introduced by Laszlo Székelyhidi and myself for the Euler equations. The methods apply for $\alpha < \frac{1}{2}$, but in order to show that they produce Leray solutions some more care is needed and in particular we must take smaller exponents. In a joint work with Maria Colombo and Luigi De Rosa we consider the Cauchy problem for the ipodissipative Navier-Stokes equations, where the classical Laplacian $-\Delta$ is substited by a fractional Laplacian $(-\Delta)^\alpha$. Although a classical Hopf approach via a Galerkin approximation shows that there is enough compactness to construct global weak solutions satisfying the energy inequality à la Leray, we show that such solutions are not ...

35Q31 ; 35A01 ; 35D30

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Research talks;Analysis and its Applications

The $T(b)$ theorem proved 30 years ago by David, Journé and Semmes, following a first result of McIntosh and Meyer, has proved to be a powerful and versatile tool for a number of applications. We will discuss history and main applications including recent ones.

42B20 ; 42B25 ; 42C40

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Research talks;Analysis and its Applications;Control Theory and Optimization

Over the past 20 years we have been interested in finding good parameterizations for sets that are well approximated by nice sets. In this talk we will discuss the meanings of good and nice. We will recall some the results from the past and present new results concerning the regularity of sets that can be well approximated by Lipschitz graphs.

28A75 ; 49Q05 ; 49Q20 ; 49Kxx

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Research talks;Partial Differential Equations;Mathematical Physics

We discuss joint work with Doug Arnold, Guy David, Marcel Filoche and Svitlana Mayboroda. Consider the Neumann boundary value problem for the operator $L = divA\nabla + V$ on a Lipschitz domain $\Omega$ and, more generally, on manifolds with and without boundary. The eigenfunctions of $L$ are often localized, as a result of disorder of the potential $V$, the matrix of coefficients $A$, irregularities of the boundary, or all of the above. In earlier work, Filoche and Mayboroda introduced the function $u$ solving $Lu = 1$, and showed numerically that it strongly reflects this localization. In this talk, we deepen the connection between the eigenfunctions and this landscape function $u$ by proving that its reciprocal $1/u$ acts as an effective potential. The effective potential governs the exponential decay of the eigenfunctions of the system and delivers information on the distribution of eigenvalues near the bottom of the spectrum. We discuss joint work with Doug Arnold, Guy David, Marcel Filoche and Svitlana Mayboroda. Consider the Neumann boundary value problem for the operator $L = divA\nabla + V$ on a Lipschitz domain $\Omega$ and, more generally, on manifolds with and without boundary. The eigenfunctions of $L$ are often localized, as a result of disorder of the potential $V$, the matrix of coefficients $A$, irregularities of the boundary, or all of the above. In ...

47A75 ; 81Vxx ; 81Q10 ; 35P20

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- ii; 423 p.
ISBN 978-2-7598-2256-0

Savoirs actuels

Localisation : Enseignement RdC (PAJO)

enseignement # espace métrique # théorie de la mesure # espace de Sobolev # théorie géométrique de la mesure # inégalité de Poincaré # groupe de Heisenberg # théorie quasi-conforme # espace euclidien # exercices

30Lxx ; 28Axx ; 30F45

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- 118 p.
ISBN 978-3-540-00001-3

Lecture notes in mathematics , 1799

Localisation : Collection 1er étage

ensemble rectifiable # théorie géométrique de la mesure # intégrale de Cauchy # capacité # opérateur de Calderon-Zygmund # courbure de Menger # problème de Painlevé

28A75 ; 28A78 ; 30C85 ; 30E20

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