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Nombre de programmes trouvés : 3322
Séminaires

le (59m36s)

Michel Ledoux - Isopérimétrie dans les espaces métriques mesurés

Le problème isopérimétrique (à volume donné, minimiser la mesure de bord, et déterminer les ensembles extrémaux), remonte aux temps les plus anciens. Tout à la fois, il peut se formuler de façon générale dans un espace métrique mesuré, et dans le même temps assez peu d’exemples explicites, en particuliers de minimiseurs, sont connus. Les questions se portent ainsi vers des propriétés de comparaison avec les des espaces modèles, comme ceux de la géométrie, euclidienne, sphérique et hyperbolique (pour lesquels les boules constituent les éléments extrémaux du problème isopérimétrique). ...
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Séminaires

le (1h5m4s)

Andras Vasy - The Feynman propagator and its positivity properties

One usually considers wave equations as evolution equations, i.e. imposes initial data and solves them. Equivalently, one can consider the forward and backward solution operators for the wave equation; these solve an equation Lu=f" style="position: relative;" tabindex="0" id="MathJax-Element-1-Frame">Lu=f, for say f" style="position: relative;" tabindex="0" id="MathJax-Element-2-Frame">f compactly supported, by demanding that u" style="position: relative;" tabindex="0" id="MathJax-Element-3-Frame">u is supported at points which are reachable by forward, respectively backward, time-like or light-like curves. This property corresponds to causality. But it has been known for a long time that in certain ...
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Cours magistraux

le (1h53m11s)

Joseph Fu - Integral geometric regularity (Part 1)

In the original form given by Blaschke in the 1930s, the famous Principal Kinematic Formula expresses the Euler characteristic of the intersection of two sufficiently regular objects in euclidean space, integrated over the space of all possible relative positions, in terms of geometric invariants associated to each of them individually. It is natural to wonder about the precise regularity needed  for this to work. The question turns on the existence of the normal cycle  of such an object A, i.e. an integral current that stands ...
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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 (1h30m6s)

Yoshihiro Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 2)

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 (1h26m57s)

Yoshihiro Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 3)

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 (1h23m9s)

Yoshihiro Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 4)

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 ...
Voir la vidéo
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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Cours magistraux

le (1h24m45s)

Tatiana Toro - Geometry of measures and applications (Part 1)

In the 1920's Besicovitch studied linearly measurable sets in the plane, that is sets with locally finite "length". The basic question he addressed was whether the infinitesimal properties of the "length" of a set E in the plane yield geometric information on E itself. This simple question marks the beginning of the study of the geometry of measures and the associated field known as Geometric Measure Theory (GMT).In this series of lectures we will present some of the main results in the area concerning ...
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Cours magistraux

le (1h19m49s)

Tatiana Toro - Geometry of measures and applications (Part 2)

In the 1920's Besicovitch studied linearly measurable sets in the plane, that is sets with locally finite "length". The basic question he addressed was whether the infinitesimal properties of the "length" of a set E in the plane yield geometric information on E itself. This simple question marks the beginning of the study of the geometry of measures and the associated field known as Geometric Measure Theory (GMT).In this series of lectures we will present some of the main results in the area concerning ...
Voir la vidéo

 
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