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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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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 (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 (50m2s)

## Robert Haslhofer - The moduli space of 2-convex embedded spheres

We investigate the topology of the space of smoothly embedded n-spheres in R^{n+1}, i.e. the quotient space M_n:=Emb(S^n,R^{n+1})/Diff(S^n). By Hatcher’s proof of the Smale conjecture, M_2 is contractible. This is a highly nontrivial theorem generalizing in particular the Schoenflies theorem and Cerf’s theorem.In this talk, I will explain how geometric analysis can be used to study the topology of M_n respectively some of its variants.I will start by sketching a proof of Smale’s theorem that M_1 is contractible. By a beautiful theorem of Grayson, the curve shortening flow deforms any closed embedded curve in the plane to a round circle, ...
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Conférences

le (51m50s)

## Melanie Rupflin - Horizontal curves of metrics and applications to geometric flows

On closed surfaces there are three basic ways to evolve a metric, by conformal change, by pull-back with diffeomorphisms and by horizontal curves, moving orthogonally to the first two types of evolution. As we will discuss in this talk, horizontal curves are very well behaved even if the underlying conformal structures degenerate in moduli space as t to T. We can describe where the metrics will have essentially settled down to the limit by time t T as opposed to regions on which the metric still has to do an infinite amount of stretching. This quantified information is essential in ...
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Conférences

le (47m37s)

## Jeff Viaclovsky - Deformation theory of scalar-flat Kahler ALE surfaces

I will discuss a Kuranishi-type theorem for deformations of complex structure on ALE Kahler surfaces, which will be used to prove that for any scalar-flat Kahler ALE surface, all small deformations of complex structure also admit scalar-flat Kahler ALE metrics. A local moduli space of scalar-flat Kahler ALE metrics can then be constructed, which is universal up to small diffeomorphisms. I will also discuss a formula for the dimension of the local moduli space in the case of a scalar-flat Kahler ALE surface which deforms to a minimal resolution of an isolated quotient singularity.  This is joint work with Jiyuan ...
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