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# Résultats de recherche

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## Co-alignement en microscopie

présentation Aurélien Dauphin Institut Curie Voir la vidéole (1h34m17s)

## P. Castillon - CAT(k)-spaces 2

The purpose of this course is to introduce the synthetic treatment of sectional curvature upper-bound on metric spaces. The basic idea of A.D. Alexandrov was to characterize the curvature bounds on the sectional curvature of a Riemannian manifold in term of properties of its distance function, and then to consider metric spaces with these properties. This approach turned out to be very fruitful and it found many applications, bringing geometric ideas to other settings. In this course we will introduce the metric spaces ... Voir la vidéole (1h28m24s)

## G. Courtois - Compactness and Finiteness Results for Gromov-Hyperbolic Spaces 2

This is a series of lectures on Bishop--Gromov's type inequalities adapted to metric spaces. We consider the case of Gromov-hyperbolic spaces and draw consequences of these inequalities such as compactness and finiteness Theorems. This course is intended to be elementary in the sense that the necessary background is described in detail. Voir la vidéole (1h21m33s)

## T. Richard - Advanced basics of Riemannian geometry 2

We will present some of the tools used by the more advanced lectures. The topics discussed will include : Gromov Hausdorff distance, comparison theorems for sectional and Ricci curvature, the Bochner formula and basics of Ricci flow. Voir la vidéole (1h27m36s)

## F. Schulze - An introduction to weak mean curvature flow 2

It has become clear in recent years that to understand mean curvature flow through singularities it is essential to work with weak solutions to mean curvature flow. We will give a brief introduction to smooth mean curvature flow and then discuss Brakke flows, their basic properties and how to establish existence via elliptic regularization. We will furthermore discuss tangent flows and regularity, and the interaction of Brakke flows with the level set flow. Time permitting, we will give an outlook on recent developments, including ... Voir la vidéole (1h25m56s)

## G. Courtois - Compactness and Finiteness Results for Gromov-Hyperbolic Spaces 3

This is a series of lectures on Bishop--Gromov's type inequalities adapted to metric spaces. We consider the case of Gromov-hyperbolic spaces and draw consequences of these inequalities such as compactness and finiteness Theorems. This course is intended to be elementary in the sense that the necessary background is described in detail. Voir la vidéole (1h30m20s)

## T. Richard - Advanced basics of Riemannian geometry 3

We will present some of the tools used by the more advanced lectures. The topics discussed will include : Gromov Hausdorff distance, comparison theorems for sectional and Ricci curvature, the Bochner formula and basics of Ricci flow. Voir la vidéole (1h35m15s)

## P. Castillon - CAT(k)-spaces 3

The purpose of this course is to introduce the synthetic treatment of sectional curvature upper-bound on metric spaces. The basic idea of A.D. Alexandrov was to characterize the curvature bounds on the sectional curvature of a Riemannian manifold in term of properties of its distance function, and then to consider metric spaces with these properties. This approach turned out to be very fruitful and it found many applications, bringing geometric ideas to other settings. In this course we will introduce the metric spaces ... Voir la vidéole (1h28m18s)