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# Résultats de recherche

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## Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 5)

In these lectures I will first recall the basic notions and results that are needed to study minimal surfaces in the smooth setting (above all the area formula and the first variation of the area), give a short review of the main (classical) techniques for existence results, and then outline the theory of Finite Perimeter Sets, including the main results of the theory (compactness, structure of distributional derivative, rectifiability). If time allows, I will conclude with a few applications. Voir la vidéole (1h24m59s)

## Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 3)

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 vidéole (1h22m41s)

## Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 4)

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 vidéole (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. Voir la vidéole (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 vidéole (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 vidéole (1h3m14s)

## Christian Gérard - Construction of Hadamard states for Klein‐Gordon fields

we will review a new construction of Hadamard states for quantized Klein-‐Gordon fields on curved spacetimes, relying on pseudo differential calculus on a Cauchy surface. We also ... Voir la vidéole (51m8s)

## Alain Bachelot - Waves in the Anti-de Sitter space-time Ads

In this talk we address some issues concerning the wave propagation in the 4D+1 anti de Sitter space time : the role of the conformal boundary, the representation of ... Voir la vidéole (55m54s)