Institut Élie Cartan de Lorraine

About: Institut Élie Cartan de Lorraine is a facility organization based out in Vandœuvre-lès-Nancy, France. It is known for research contribution in the topics: Boundary value problem & Stochastic differential equation. The organization has 345 authors who have published 1084 publications receiving 15512 citations. The organization is also known as: Institut Élie-Cartan de Nancy.

Threefolds with quasi-projective universal cover

Abstract: We study compact Kahler threefolds X with infinite fundamental group whose universal cover can be compactified. Combining techniques from L 2 -theory, Campana's geometric orbifolds and the minimal model program we show that this condition imposes strong restrictions on the geometry of X. In particular we prove that if a projective threefold with infinite fundamen- tal group has a quasi-projective universal cover ~ X, then ~ X is isomorphic to the product of an ane space of positive dimension with a simply connected projective manifold.

Weak solution of semi-linear PDE, BSDE and homogenization

Abstract: The sketch of the proof using BSDE of a homogenization result for semi-linear PDE with a divergence-form operator is given here. The method employed here relies on the use of a weak topology.

Maximal representations of uniform complex hyperbolic lattices in exceptional Hermitian Lie groups

Abstract: We complete the classification of maximal representations of uniform complex hyperbolic lattices in Hermitian Lie groups by dealing with the exceptional groups ${\rm E}_6$ and ${\rm E}_7$. We prove that if $\rho$ is a maximal representation of a uniform complex hyperbolic lattice $\Gamma\subset{\rm SU}(1,n)$, $n>1$, in an exceptional Hermitian group $G$, then $n=2$ and $G={\rm E}_6$, and we describe completely the representation $\rho$. The case of classical Hermitian target groups was treated by Vincent Koziarz and the second named author (arxiv:1506.07274). However we do not focus immediately on the exceptional cases and instead we provide a more unified perspective, as independent as possible of the classification of the simple Hermitian Lie groups. This relies on the study of the cominuscule representation of the complexification of the target group. As a by product of our methods, when the target Hermitian group $G$ has tube type, we obtain an inequality on the Toledo invariant of the representation $\rho:\Gamma\rightarrow G$ which is stronger than the Milnor-Wood inequality (thereby excluding maximal representations in such groups).

Non-positively curved Ricci Surfaces with catenoidal ends

Abstract: A Ricci surface is defined to be a Riemannian surface $$({\varvec{M}},{\varvec{g}}_{\varvec{M}})$$ whose Gauss curvature $${\varvec{K}}$$ satisfies the differential equation $${\varvec{K}}\varvec{\Delta } {\varvec{K}} + {\varvec{g}}_{\varvec{M}}\left( {{\textbf {d}}{\varvec{K}}},{{\textbf {d}}{\varvec{K}}}\right) + {\textbf {4}}{\varvec{K}}^{\textbf {3}}={\textbf {0}}$$ . In the case where $${\varvec{K}}<{\textbf {0}}$$ , this equation is equivalent to the well-known Ricci condition for the existence of minimal immersions in $${\mathbb {R}}^3$$ . Recently, Andrei Moroianu and Sergiu Moroianu proved that a Ricci surface with non-positive Gauss curvature admits locally an isometric minimal immersion into $${\mathbb {R}}^3$$ . In this paper, we are interested in studying non-compact orientable Ricci surfaces with non-positive Gauss curvature. Firstly, we give a definition of catenoidal end for non-positively curved Ricci surfaces. Secondly, we develop a tool which can be regarded as an analogue of the Weierstrass data to obtain some classification results for non-positively curved Ricci surfaces of genus zero with catenoidal ends. Furthermore, we also give an existence result for non-positively curved Ricci surfaces of arbitrary positive genus which have finite catenoidal ends.

Non annulation des fonctions L automorphes au point central

Abstract: The question about modular forms have recently received a lot of attention; concerning the non-vanishing of automorphic L-functions Michel, Kowalski and Vanderkam proved (among others results) that there's positive proportion of non-vanishing of primitives forms at the critical point. This result was proved by these authors in the prime level case; on the othe hand, Iwaniec, Luo and Sarnak showed the same result for the squarefree level case. In order to understand the influence of the arithmetic shape of level forms in their vanishing, this paper studies a generalisation to the primitives forms with prime powers level.