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Institut Fourier

L’Institut Fourier, laboratoire de mathématiques de Grenoble, est une unité mixte de recherche CNRS/Université Grenoble Alpes. Ses activités portent principalement sur les mathématiques fondamentales développées autour de six grands thèmes de recherche : algèbre et géométries, combinatoire et didactique, géométrie et topologie, physique mathématique, probabilités, théorie des nombres. Ses recherches s’ouvrent aussi à d’autres disciplines, telles que la biologie, l’informatique et la physique. Depuis 2011, l’Institut Fourier filme ses évènements scientifiques tels que : colloques, séminaires, écoles d’été, conférences grand public, …

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Liste des programmes

I will discuss certain invariants of singularities, the Hodge ideals, that are defined in the context of Saito’s theory of mixed Hodge modules. They can be considered as higher order analogues of the multiplier ideals, invariants that have had a lot of applications in complex geometry. I will describe some general ...
I will discuss a method that we recently introduced in collaboration with Chu and Weinkove which gives interior C1,1 estimates for the non-degenerate complex Monge-Ampère equation on compact Kähler manifolds (possibly with boundary). The method is sufficiently robust to also give C1,1 regularity of geodesic segments in the space of ...
There at least three families of hyper-K ̈ahler manifolds built from cubic fourfolds, the most recently discovered one being the compactified intermediate Jacobian fibrations I constructed with Laza and Sacca. In a joint work with Koll ́ar, Laza and Sacca, we provide an easy way to compute their deformation ...
This is a talk about my works with Damin Wu concerning those manifolds with negative holomorphic sectional curvature. I shall describe our theorem that such manifold must have negative first Chern class.
Consider any meromorphic family of endomorphisms of the complex projective plane parameterized by the punctured unit disk. We shall explain how to describe the behaviour of their measures of maximal entropy when one approaches the central fiber. This generalizes works by Demarco and Faber.
Using and extending an approximation process due to Berman, we show that the quasi-psh envelope of a viscosity super-solution is a pluripotential super-solution of a given complex Monge-Ampère equation. We apply these ideas to Kahler-Einstein geometry (joint work with H.C.Lu and A.Zeriahi).
We investigate the holonomy group of singular Kähler-Einstein metrics on klt varieties with numerically trivial canonical divisor. Finiteness of the number of connected components, a Bochner principle for holomorphic tensors, and a connection between irreductibility of holonomy representations and stability of the tangent sheaf are established. As a consequence, we ...
Monge-Ampère and Hessian equations on compact Hermitian manifolds
Linearly saturated subvarieties on uniruled projective manifolds
 
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