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# Résultats de recherche

**800**

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## Laurent Mazet - Minimal hypersurfaces of least area

In this talk, I will present a joint work with H. Rosenberg where we give a characterization of the minimal hypersurface of least area in any Riemannian manifold. As a consequence, we give a lower bound for the area of a minimal surface in a hyperbolic 3-manifold. 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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## Igor Belegradek - Smoothness of Minkowski sum and generic rotations

I will discuss whether the Minkowski sum of two compact convex bodies can be made smoother by a generic rotation of one of them. Here "generic" is understood in the sense of Baire category. The main result is a construction of an infinitely differentiable convex plane domain whose Minkowski sum with any generically rotated copy of itself is not five times differentiable. Voir la vidéole (1h4m1s)

## Feng Luo - Discrete conformal geometry of polyhedral surfaces and its convergence

Our recent joint work with D. Gu established a discrete version of the uniformization theorem for compact polyhedral surfaces. In this talk, we prove that discrete uniformizaton maps converge to conformal maps when the triangulations are sufficiently fine chosen. We will also discuss the relationship between the discrete uniformization theorem and convex polyhedral surfaces in the hyperbolic 3-space. This is a joint work with J. Sun and T. Wu. Voir la vidéole (58m50s)