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Nombre de programmes trouvés : 5587
Cours magistraux

le (1h20m15s)

P. Castillon - CAT(k)-spaces 4

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 ...
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Cours magistraux

le (0s)

F. Schulze - An introduction to weak mean curvature flow 4

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 ...
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Séminaires

le (1h58m54s)

Explorer les correspondances numériques: quels outils et quelles pratiques ?

La plate-forme EMAN (35 projets hébergés) rassemble désormais neuf projets d’éditorialisation de correspondances d’auteurs du XVIIIe au XXe siècles, objets de questionnements littéraires et historiques. Les expériences éditoriales menées depuis 2015 sur la plate-forme EMAN ont conduit à la constitution du groupe de travail « Correspondance » en visant des échanges entre praticiens afin d’interroger les enjeux du numérique pour le renouvellement des études épistolaires et des méthodes éditoriales. Ce webinaire cherche donc à envisager les corpus de correspondance des domaines littéraires, scientifiques et historiques et leurs éditions ...
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Cours magistraux

le (1h31m43s)

R. Bamler - Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 1

I will present recent work with Kleiner in which we verify two topological conjectures using Ricci flow. First, we classify the homotopy type of every 3-dimensional spherical space form. This proves the Generalized Smale Conjecture and gives an alternative proof of the Smale Conjecture, which was originally due to Hatcher. Second, we show that the space of metrics with positive scalar curvature on every 3-manifold is either contractible or empty. This completes work initiated by Marques. At the heart of our proof is a new ...
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Cours magistraux

le (1h46m5s)

A. Mondino - Metric measure spaces satisfying Ricci curvature lower bounds 1

The idea of compactifying the space of Riemannian manifolds satisfying Ricci curvature lower bounds goes back to Gromov in the '80ies and was pushed by Cheeger-Colding in the ‘90ies, who investigated the structure of spaces arising as Gromov-Hausdorff limits of smooth Riemannian manifolds satisfying Ricci curvature lower bounds. A completely new approach based on Optimal Transport was proposed by Lott-Villani and Sturm around ten years ago; via this approach, one can give a precise sense of what means for a non-smooth space (more precisely ...
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Cours magistraux

le (1h23m9s)

A. Song - What is the (essential) minimal volume? 1

I will discuss the notion of minimal volume and some of its variants. The minimal volume of a manifold is defined as the infimum of the volume over all metrics with sectional curvature between -1 and 1. Such an invariant is closely related to "collapsing theory", a far reaching set of results developed by Cheeger, Gromov, Fukaya and others to describe bounded sectional curvature metrics. Most of my talks will be focused on presenting the main aspects of this theory: thick-thin decomposition, F-structures and ...
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Cours magistraux

le (1h21m33s)

C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 1

We introduce various notions of convergence of Riemannian manifolds and metric spaces.  We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature.   We close the course by presenting methods and theorems that may be applied to prove these open questions including older techniques developed with Lakzian, with Huang and Lee, and with Portegies.  I will also present key new results of Allen and Perales.   Students and postdocs interested in ...
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Cours magistraux

le (1h31m25s)

R. Bamler - Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 2

I will present recent work with Kleiner in which we verify two topological conjectures using Ricci flow. First, we classify the homotopy type of every 3-dimensional spherical space form. This proves the Generalized Smale Conjecture and gives an alternative proof of the Smale Conjecture, which was originally due to Hatcher. Second, we show that the space of metrics with positive scalar curvature on every 3-manifold is either contractible or empty. This completes work initiated by Marques. At the heart of our proof is a new ...
Voir la vidéo
Cours magistraux

le (1h44m17s)

A. Mondino - Metric measure spaces satisfying Ricci curvature lower bounds 2

The idea of compactifying the space of Riemannian manifolds satisfying Ricci curvature lower bounds goes back to Gromov in the '80ies and was pushed by Cheeger-Colding in the ‘90ies, who investigated the structure of spaces arising as Gromov-Hausdorff limits of smooth Riemannian manifolds satisfying Ricci curvature lower bounds. A completely new approach based on Optimal Transport was proposed by Lott-Villani and Sturm around ten years ago; via this approach, one can give a precise sense of what means for a non-smooth space (more precisely ...
Voir la vidéo
Cours magistraux

le (1h23m9s)

A. Song - What is the (essential) minimal volume? 2

I will discuss the notion of minimal volume and some of its variants. The minimal volume of a manifold is defined as the infimum of the volume over all metrics with sectional curvature between -1 and 1. Such an invariant is closely related to "collapsing theory", a far reaching set of results developed by Cheeger, Gromov, Fukaya and others to describe bounded sectional curvature metrics. Most of my talks will be focused on presenting the main aspects of this theory: thick-thin decomposition, F-structures and ...
Voir la vidéo

 
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