Prochainement

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Mercredi 1er juillet 16:00-18:00 Louis Ioos  (Tel Aviv)
Applications of Berezin-Toeplitz quantization to Donaldson’s program in Kähler geometry

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Lieu : Demander le lien Zoom à jean-michel.bismut@u-psud.fr

Résumé : I will show how Berezin-Toeplitz quantization can be used to simplify and extend Donaldson’s proof
of existence and smooth convergence of balanced metrics to the Kähler metric of constant scalar curvature on a polarized manifold. This is of specific interest in the case of canonically balanced metrics converging to the polarized Kähler-Einstein metric, where only weak convergence results were known. I will then show how this allows to compute the rate of convergence of Donaldson’s iterations to the balanced product in various settings.
This approach is based in particular on the asymptotics of the spectral gap of the Berezin transform, which were computed in a joint work with V. Kaminker, L. Polterovich and D. Shmoish.

Applications of Berezin-Toeplitz quantization to Donaldson’s program in Kähler geometry  Version PDF


Mercredi 24 juin 16:00-18:00 François Labourie  (Université de Nice)
Plateau problems for maximal surfaces in pseudo-hyperbolic spaces

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Lieu : Demander le lien Zoom à jean-michel.bismut@u-psud.fr

Résumé : The pseudo-hyperbolic space $H^2,n$ is in many ways a generalisation of the hyperbolic space. It is a pseudo-Riemannian manifold with signature (2,n) with constant curvature, it also has a « boundary at infinity ». We explain in this joint work with Jérémy Toulisse and Mike Wolf how special curves in this boundary at infinity, bounds unique maximal surfaces in H^2,n. The result bears some analogy with the Cheng-Yau existence results for affine spheres tangent to convex curves in the projective plane. The talk will spend sometime explainig the geometry of the pseudo-hyperbolic space and its boundary at infinity, as well as description of maximal surfaces. If time permits, I will explain some extension to « quasi-periodic » maximal surfaces in H^2,n.

Plateau problems for maximal surfaces in pseudo-hyperbolic spaces  Version PDF

Mercredi 17 juin 16:00-18:00 H.-J. Hein  (Münster)
Classification of asymptotically conical Calabi-Yau manifolds

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Lieu : Demander le lien Zoom à jean-michel.bismut@u-psud.fr

Résumé : In this talk I will explain how to construct and classify all complete Calabi-Yau manifolds that are polynomially asymptotic to some given Calabi-Yau cone (with a smooth cross-section) at infinity. If the Reeb vector field of the cone generates a circle action, this result goes back to joint work with Ronan Conlon in 2014. In more recent joint work we were able to remove the assumption about the Reeb vector field. This now allows us to give a complete analysis of the most interesting class of examples - smoothings of cones over irregular Sasaki-Einstein manifolds - where only one sporadic example was known previously.

Classification of asymptotically conical Calabi-Yau manifolds  Version PDF


Mercredi 10 juin 16:00-18:00 Yang Li  (IAS (Princeton))
Weak SYZ conjecture for hypersurfaces in the Fermat family

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Lieu : Demander le lien zoom à jean-michel.bismut@u-psud.fr

Résumé : The SYZ conjecture predicts that for polarised Calabi-Yau
manifolds undergoing the large complex structure limit, there should be
a special Lagrangian torus fibration. A weak version asks if this
fibration can be found in the generic region. I will discuss my recent
work proving this weak SYZ conjecture for the degenerating hypersurfaces
in the Fermat family. Although these examples are quite special, this is
the first construction of generic SYZ fibrations that works uniformly in
all complex dimensions.

Weak SYZ conjecture for hypersurfaces in the Fermat family  Version PDF