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Nombre de programmes trouvés : 4325
Conférences

le (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.
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Conférences

le (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.
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Conférences

le (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.
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Conférences

le (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.
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Conférences

le (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.
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Conférences

le (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.
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Conférences

le (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 3-manifolds due to Brock-Bromberg one obtains explicit upper bounds for the volume of a mapping torus in terms of the translation distance of the monodromy on Teichmueller space. We will explain Brock-Bromberg's approach to the Thurston's uniformization theorem for hyperbolic manifolds which are mapping tori. In particular the "coarse geometry" of the convex core of a quasi fuchsian manifold.
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