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Conférences

le (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.
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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 (48m45s)

## 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.
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Conférences

le (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.
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Conférences

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.
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