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Nombre de programmes trouvés : 2807
Cours magistraux

le (52m2s)

A. Lytchak - Convex subsets in generic manifolds

In the talk I would like to discuss some  statements and questions about convex subsets and convex hulls in generic Riemannian manifolds of dimension at least 3. The statements, obtained jointly with Anton Petrunin,  are elementary but somewhat  surprising for the Euclidean intuition. For instance, the convex hull of any finite non-collinearset  turns out to be  either   the whole manifold or non-closed.
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le (56m54s)

A. Song - On the essential minimal volume of Einstein 4-manifolds

Given a positive epsilon, a closed Einstein 4-manifold admits a natural thick-thin decomposition. I will explain how, for any delta, one can modify the Einstein metric to a bounded sectional curvature metric so that the thick part has volume linearly bounded by the Euler characteristic and the thin part has injectivity radius less than delta. I will also discuss relations to conjectural obstructions to collapsing with bounded sectional curvature or to the existence of Einstein metrics.
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Cours magistraux

le (1h36m19s)

C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 4

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 (57m40s)

R. Bamler - Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 4

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 (1h44m27s)

A. Mondino - Metric measure spaces satisfying Ricci curvature lower bounds 4

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 (1h25m35s)

A. Song - What is the (essential) minimal volume? 4

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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