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Cours magistraux

le (1h10m1s)

## Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 5)

A celebrated theorem of Almgren shows that every integer rectifiable current which minimizes (locally) the area is a smooth submanifold except for a singular set of codimension at most 2. Almgren’s theorem is sharp in codimension higher than 1, because holomorphic subvarieties of Cn are area-minimizing. In fact the typical singularity of a 2-dimensional area-minimizing current is modelled by branch points of holomorphic curves. These singularities are rather difficult to analyze because they might be very high order phenomena.
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Cours magistraux

le (1h50m6s)

## Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 1)

A celebrated theorem of Almgren shows that every integer rectifiable current which minimizes (locally) the area is a smooth submanifold except for a singular set of codimension at most 2. Almgren’s theorem is sharp in codimension higher than 1, because holomorphic subvarieties of Cn are area-minimizing. In fact the typical singularity of a 2-dimensional area-minimizing current is modelled by branch points of holomorphic curves. These singularities are rather difficult to analyze because they might be very high order phenomena.
Voir la vidéo
Cours magistraux

le (1h25m25s)

## Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 2)

A celebrated theorem of Almgren shows that every integer rectifiable current which minimizes (locally) the area is a smooth submanifold except for a singular set of codimension at most 2. Almgren’s theorem is sharp in codimension higher than 1, because holomorphic subvarieties of Cn are area-minimizing. In fact the typical singularity of a 2-dimensional area-minimizing current is modelled by branch points of holomorphic curves. These singularities are rather difficult to analyze because they might be very high order phenomena.
Voir la vidéo
Cours magistraux

le (1h14m50s)

## Valérie Berthé - Fractions continues multidimensionnelles et dynamique (Part 2)

Le but de cet exposé est de présenter des généralisations multidimensionnelles des fractions continues et de l’algorithme d’Euclide d’un point de vue systèmes dynamiques, en nous concentrant sur les liens avec la numération et les substitutions. Nous allons considérer principalement deux types de généralisations, à savoir, les algorithmes définis par homographies, comme l’algorithme de Jacobi-Perron, et les fractions continues associées aux algorithmes de réduction dans les réseaux.
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