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# Résultats de recherche

**757**

le (50m52s)

## D. Brotbek - On the hyperbolicity of general hypersurfaces

A smooth projective variety over the complex numbers is said to be (Brody) hyperbolic if it doesn’t contain any entire curve. Kobayashi conjectured in the 70’s that general hypersurfaces of sufficiently large degree in PN are hyperbolic. This conjecture was only recently proved by Siu. The purpose of this talk is to present a new proof of this conjecture. The main idea of the proof, based on the theory of jet differential equations, is to establish that a stronger property, open in the Zariski topology, ... Voir la vidéole (52m41s)

## F. Campana - Birational stability of the orbifold cotangent bundle

We show that a foliation on a projective complex manifold is algebraic with rationally connected (closure of) leaves exactly when its minimal slope with respect to some movable class is positive. This extends and strengthens former classical results by Y. Miyaoka and Bogomolov-McQuillan. Applications to foliations, hyperbolicity (a converse to a result of JP. Demailly) and moduli will be mentioned.This is a joint work with Mihai Paun, partly based on a former joint work with T. Voir la vidéole (51m42s)

## S. Donaldson - Boundary value problems for $G_2$ structures

In the lecture we consider the existence of G2 structures on 7-manifolds with boundary, with prescribed data on the boundary. In the first part we will review general background and theory, including Hitchin’s variational approach. We will then discuss in more detail reductions of the problem in the presence of symmetry and in ”adiabatic limits”, and connections with real and complex Monge-Ampère equations. Voir la vidéole (49m10s)

## C. Favre - Degeneration of measures of maximal entropy

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. Voir la vidéole (32m18s)

## V. Guedj - Quasi-psh envelopes and supersolutions

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). Voir la vidéole (48m55s)

## S. Kebekus - Varieties with vanishing first Chern class

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 show that up to finite quasi-étale covers, varieties with strongly stable tangent sheaf are either Calabi-Yau (CY) or irreducible holomorphic symplectic (IHS). Finally, finiteness properties of fundamental groups of CY and IHS varieties are ... Voir la vidéole (52m3s)

## N. Mok - Linearly saturated subvarieties on uniruled projective manifolds

Linearly saturated subvarieties on uniruled projective manifolds Voir la vidéole (51m24s)

## M. Mustata - Hodge ideals

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 properties of Hodge ideals and some applications. This is joint work with Mihnea Popa. Voir la vidéole (58m27s)