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# Résultats de recherche

**750**

le (58m50s)

## Stéphane Saboureau - Sweep-outs, width estimates and volume

Sweep-out techniques in geometry and topology have recently received a great deal of attention, leading to major breakthroughs. In this talk, we will present several width estimates relying on min-max arguments in relation to the volume of Riemannian manifolds. Dealing with the case of surfaces first, we will focus our attention on generalisations in higher dimension and present new estimates obtained in a work in progress. Voir la vidéole (1h3m4s)

## Jean-Marc Schlenker - Anti-de Sitter geometry and polyhedra inscribed in quadrics

Anti-de Sitter geometry is a Lorentzian analog of hyperbolic geometry. In the last 25 years a number of connections have emerged between 3-dimensional anti-de Sitter geometry and the geometry of hyperbolic sufaces. We will explain how the study of ideal polyhedra in anti-de Sitter space leads to an answer to a question of Steiner (1832) on the combinatorics of polyhedra that can be inscribed in a quadric. Joint work with Jeff Danciger and Sara Maloni. Voir la vidéole (52m51s)

## Burkhard Wilking - Manifolds with almost nonnegative curvature operator

We show that n-manifolds with a lower volume bound v and upper diameter bound D whose curvature operator is bounded below by $-\varepsilon(n,v,D)$ also admit metrics with nonnegative curvature operator. The proof relies on heat kernel estimates for the Ricci flow and shows that various smoothing properties of the Ricci flow remain valid if an upper curvature bound is replaced by a lower volume bound. nonnegative curvature operator. Voir la vidéole (1h1m10s)

## Vladimir Markovic - Harmonic quasi-isometries between negatively curved manifolds

Very recently, Markovic, Lemm-Markovic and Benoist-Hulin, established the existence of a harmonic mapping in the homotopy class of an arbitrary quasi-isometry between rank 1 symmetric spaces. I will discuss these results and the more general conjecture which states that this result holds for quasi-isometries between negatively curved manifolds and metric spaces. Voir la vidéole (1h37s)

## Juan Souto - Counting curves on surfaces

An old theorem of Huber asserts that the number of closed geodesics of length at most L on a hyperbolic surface is asymptotic to $\frac{e^L}L$. However, things are less clear if one either fixes the type of the curve, possibly changing the notion of length, or if one counts types of curves. Here, two curves are of the same type if they differ by a mapping class. I will describe some results in these directions. Voir la vidéole (45m38s)

## Genevieve Walsh - Boundaries of Kleinian groups

We study the problem of classifying Kleinian groups via the topology of their limit sets. In particular, we are interested in one-ended convex-cocompact Kleinian groups where each piece in the JSJ decomposition is a free group, and we describe interesting examples in this situation. In certain cases we show that the type of Kleinian group is determined by the topology of its group boundary. We conjecture that this is not the case in general. We also determine the homeomorphism types of planar boundaries that can occur. This is joint work in progress with Peter Haissinsky and Luisa Paoluzzi. Voir la vidéole (1h1m46s)

## David Gabai - Maximal cusps of low volume

With Robert Haraway, Robert Meyerhoff, Nathaniel Thurston and Andrew Yarmola.We address the following question. What are all the 1-cusped hyperbolic 3-manifolds whose maximal cusps have low volume? Among other things we will outline a proof that the figure-8 knot complement and its sister are the 1-cusped manifolds with minimal maximal cusp volume. Voir la vidéole (1h5s)

## Greg McShane - Volumes of hyperbolics manifolds and translation distances

...Schlenker and Krasnov have established a remarkable Schlaffli-type formula for the (renormalized) volume of a quasi-Fuchsian manifold. Using this, some classical results in complex*analysis*and Gromov-Hausdorff convergence for sequences of open... Voir la vidéo

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