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# Résultats de recherche

**750**

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## Robert Young - Quantitative geometry and filling problems (Part 3)

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 (1h29m18s)

## Gilles Courtois - The Margulis lemma, old and new (Part 5)

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 (1h30m40s)

## Feng Luo - An introduction to discrete conformal geometry of polyhedral surfaces (Part 4)

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 (1h23m14s)

## Robert Young - Quantitative geometry and filling problems (Part 4)

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 (1h28m36s)

## Robert Young - Quantitative geometry and filling problems (Part 5)

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 (1h25m8s)

## Feng Luo - An introduction to discrete conformal geometry of polyhedral surfaces (Part 5)

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 (56m16s)

## Reto Buzano - Minimal hypersurfaces with bounded index and bounded area

We study sequences of closed minimal hypersurfaces (in closed Riemannian manifolds) that have uniformly bounded index and area. In particular, we develop a bubbling result which yields a bound on the total curvature along the sequence. As a consequence, we obtain qualitative control on the topology of minimal hypersurfaces in terms of index and area. This is joint work with Ben Sharp. Voir la vidéole (50m14s)

## Sa'ar Hersonsky - Electrical Networks and Stephenson's Conjecture

The Riemann Mapping Theorem asserts that any simply connected planar domain which is not the whole of it, can be mapped by a conformal homeomorphism onto the open unit disk. After normalization, this map is unique and is called the Riemann mapping. In the 90's, Ken Stephenson, motivated by a circle packing approximation scheme suggested by Thurston (and first proved to converge by Rodin-Sullivan), predicted that the Riemann Mapping may be approximated by a different scheme, i.e., by a sequence of finite networks endowed with particular choices of conductance constants. These networks are naturally defined in terms of the contact ... Voir la vidéole (50m24s)