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# Résultats de recherche

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## Feng Luo - An introduction to discrete conformal geometry of polyhedral surfaces (Part 1)

The goal of the course is to introduce some of the recent developments on discrete conformal geometry of polyhedral surfaces. We plan to cover the following topics.- The Andreev-Koebe-Thurston theorem on circle packing polyhedral metrics and Marden-Rodin’s proof- Thurston’s conjecture on the convergence of circle packings to the Riemann mapping and its solution by Rodin-Sullivan- Finite dimensional variational principles associated to polyhedral surfaces- A discrete conformal equivalence of polyhedral surfaces and its relationship to convex polyhedra in hyperbolic 3-space- A discrete uniformization theorem for compact polyhedral surfaces- Convergence of discrete conformality and some open problems Voir la vidéole (1h25m39s)

## Robert Young - Quantitative geometry and filling problems (Part 2)

Plateau's problem asks whether there exists a minimal surface with a given boundary in Euclidean space. In this course, we will study related problems in broader classes of spaces and ask what the asymptotics of filling problems tell us about the geometry of surfaces in groups and spaces. What do minimal and nearly minimal surfaces look like in different spaces, and how is the geometry of surfaces related to the geometry of the ambient space? Our main examples will arise from geometric group theory, including nilpotent groups and symmetric spaces. Voir la vidéole (1h27m31s)

## Gilles Courtois - The Margulis lemma, old and new (Part 1)

The Margulis lemma describes the structure of the group generated by small loops in the fundamental group of a Riemannian manifold, thus giving a picture of its local topology. Originally stated for homogeneous spaces by C. Jordan, L. Bieberbach, H. J. Zassenhaus, D. Kazhdan-G. Margulis, it has been extended to the Riemannian setting by G. Margulis for manifolds of non positive curvature. The goal of these lectures is to present the recent work of V. Kapovitch and B. Wilking who gave a sharp version of the Margulis lemma under the assumption that the Ricci curvature is bounded below. Their method ... Voir la vidéole (1h31m39s)

## Robert Young - Quantitative geometry and filling problems (Part 1)

Plateau's problem asks whether there exists a minimal surface with a given boundary in Euclidean space. In this course, we will study related problems in broader classes of spaces and ask what the asymptotics of filling problems tell us about the geometry of surfaces in groups and spaces. What do minimal and nearly minimal surfaces look like in different spaces, and how is the geometry of surfaces related to the geometry of the ambient space? Our main examples will arise from geometric group theory, including nilpotent groups and symmetric spaces. Voir la vidéole (1h23m25s)

## Laurent Mazet - Some aspects of minimal surface theory (Part 5)

In a Riemannian 3-manifold, minimal surfaces are critical points of the area functional and can be a useful tool to understand the geometry and the topology of the ambient manifold. The aim of these lectures is to give some basic definitions about minimal surface theory and present some results about the construction of minimal surfaces in Riemannian 3-manifolds. Voir la vidéole (1h2m59s)

## Decision making at scale: Algorithms, Mechanisms, and Platforms

YouTube competes with Hollywood as an entertainment channel, and also supplements Hollywood by acting as a distribution mechanism. Twitter has a similar relationship to news media, and Coursera to Universities. But there are no online alternatives for making democratic decisions at large scale as a society. In this talk, we will describe two algorithmic approaches towards large scale decision making that we are exploring. a) Knapsack voting and participatory budgeting: All budget problems are knapsack problems at their heart, since the goal is ... Voir la vidéole (1h29m43s)

## Laurent Mazet - Some aspects of minimal surface theory (Part 4)

In a Riemannian 3-manifold, minimal surfaces are critical points of the area functional and can be a useful tool to understand the geometry and the topology of the ambient manifold. The aim of these lectures is to give some basic definitions about minimal surface theory and present some results about the construction of minimal surfaces in Riemannian 3-manifolds. Voir la vidéole (1h14m35s)

## Thomas Richard - Lower bounds on Ricci curvature, with a glimpse on limit spaces (Part 5)

The goal of these lectures is to introduce some fundamental tools in the study of manifolds with a lower bound on Ricci curvature. We will first state and prove the laplacian comparison theorem for manifolds with a lower bound on the Ricci curvature, and derive some important consequences : Bishop-Gromov inequality, Myers theorem, Cheeger-Gromoll splitting theorem. Then we will define the Gromov-Hausdorff distance between metric spaces which will allow us to consider limits of sequences of Riemannian manifolds, along the way we will prove ... Voir la vidéole (1h10m42s)