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.

Maximum Principle and Bang-Bang Property of Time Optimal Controls for Schrödinger-Type Systems

Abstract: We consider the time optimal control problem, with a point target, for a class of infinite dimensional systems with a dynamics governed by an abstract Schrodinger type equation. The main results establish a Pontryagyn type maximum principle and give sufficient conditions for the bang-bang property of optimal controls. The results are then applied to some systems governed by partial differential equations. The paper ends by a discussion of possible extensions and by stating some open problems.

From stochastic, individual-based models to the canonical equation of adaptive dynamics in one step

Abstract: We consider a model for Darwinian evolution in an asexual population with a large but non-constant populations size characterized by a natural birth rate, a logistic death rate modelling competition and a probability of mutation at each birth event. In the present paper, we study the long-term behavior of the system in the limit of large population ($K\rightarrow\infty$) size, rare mutations ($u\rightarrow 0$), and small mutational effects ($\sigma\rightarrow 0$), proving convergence to the canonical equation of adaptive dynamics (CEAD). In contrast to earlier works, e.g. by Champagnat and Meleard, we take the three limits simultaneously, i.e. $u=u_K$ and $\sigma=\sigma_K$, tend to zero with $K$, subject to conditions that ensure that the time-scale of birth and death events remains separated from that of successful mutational events. This slows down the dynamics of the microscopic system and leads to serious technical difficulties that requires the use of completely different methods. In particular, we cannot use the law of large numbers on the diverging time needed for fixation to approximate the stochastic system with the corresponding deterministic one. To solve this problem we develop a "stochastic Euler scheme" based on coupling arguments that allows to control the time evolution of the stochastic system over time-scales that diverge with $K$.

Rationally connected manifolds and semipositivity of the Ricci curvature

Abstract: This work establishes a structure theorem for compact Kahler manifolds with semipositive anticanonical bundle. Up to finite etale cover, it is proved that such manifolds split holomorphically and isometrically as a product of Ricci flat varieties and of rationally connected manifolds. The proof is based on a characterization of rationally connected manifolds through the non existence of certain twisted contravariant tensor products of the tangent bundle, along with a generalized holonomy principle for pseudoeffective line bundles. A crucial ingredient for this is the characterization of uniruledness by the property that the anticanonical bundle is not pseudoeffective.

Tenseur d'impulsion-énergie et Feuilletages

Abstract: Le sujet principal de cette these est d'interpreter le tenseur d'impulsion-energie dans le cadre des feuilletages. On s'interesse dans un premier temps a la geometrie spinorielle transverse, i.e. celle du fibre normal. On definit l'operateur de Dirac basique sur un feuilletage riemannian et on etablit une formule de type Schrodinger-Lichnerowicz. On donne ainsi des inegalites de type Friedrich et de type Kirchberg dans le cas d'un feuilletage kahlerien et une estimation dans le cas d'un feuilletage kahler-quaternionien. Le cas des flots riemanniens va permettre de mieux comprendre le tenseur d'impulsion-energie dans le cadre des feuilletages. Il apparait comme un tenseur naturel antisymetrique permettant de le voir comme le tenseur d'O'Neill du flot. Finalement, on caracterise le cas de dimension 3 par une solution de l'equation de Dirac.

Operator Calculus on Graphs: Theory and Applications in Computer Science

Abstract: Combinatorial Algebras and Their Properties Combinatorics and Graph Theory Operator Calculus Probability on Algebraic Structures Computational Complexity Symbolic Computations Using Mathematica.