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# Résultats de recherche

**4325**

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## 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 (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 (55m16s)

## Robert Young - Quantitative rectifiability and differentiation in the Heisenberg group

(joint work with Assaf Naor) The Heisenberg group $\mathbb{H}$ is a sub-Riemannian manifold that is unusually difficult to embed in $\mathbb{R}^n$. Cheeger and Kleiner introduced a new notion of differentiation that they used to show that it does not embed nicely into $L_1$. This notion is based on surfaces in $\mathbb{H}$, and in this talk, we will describe new techniques that let us quantify the "roughness" of such surfaces, find sharp bounds on the distortion of embeddings of $\mathbb{H}$, and estimate the accuracy of an approximate algorithm for the Sparsest Cut Problem. 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 (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 (50m24s)

## Daniel Ketover - Sharp entropy bounds of closed surfaces and min-max theory

In 2012, Colding-Ilmanen-Minicozzi-White conjectured that the entropy of any closed surface in R^3 is at least that of the self-shrinking two-sphere. I will explain joint work with X. Zhou where we interpret this conjecture as a parabolic version of the Willmore problem and give a min-max proof of (most cases) of their conjecture. Voir la vidéole (54m55s)

## 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 (1h5s)