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.

Stochastic analysis of emergence of evolutionary cyclic behavior in population dynamics with transfer

Abstract: Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance We consider a stochastic model for the evolution of a discrete population structured by a trait taking finitely many values, with density-dependent competition Traits are vertically inherited unless a mutation occurs, and can also be horizontally transferred by unilateral conjugation with frequency dependent rate Our goal is to analyze the trade-off between natural evolution to higher birth rates and transfer, which drives the population towards lower birth rates Simulations show that evolutionary outcomes include evolutionary suicide or cyclic re-emergence of small populations with well-adapted traits We focus on a parameter scaling where individual mutations are rare but the global mutation rate tends to infinity This implies that negligible sub-populations may have a strong contribution to evolution Our main result quantifies the asymptotic dynamics of subpopulation sizes on a logarithmic scale We characterize the possible evolutionary outcomes with explicit criteria on the model parameters An important ingredient for the proofs lies in comparisons of the stochastic population process with linear or logistic birth-death processes with immigration For the latter processes, we derive several results of independent interest

Opérateurs invariants sur certains immeubles affines de rang 2

Abstract: We consider a building $\Delta$ of type $\widetilde A_2$ or $\widetilde B_2$, different subsets $S'$ of vertices in $\Delta$ and different automorphism groups $G$, very strongly transitive on $\Delta$. We prove that the algebra of $G-$invariant operators acting on the space of functions on $S'$ is often not commutative (contrarily to the classical results). In some cases we describe its structure, determine its radial eigenfunctions and deduce that the Helgason conjecture (about the Poisson transform) is not verified in this context.

Dynamical Systems and Uniform Distribution of Sequences

Abstract: We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for establishing multidimensional van der Corput sets. This condition is applied to various examples.

Hyperbolicity and specialness of symmetric powers

Abstract: Inspired by the computation of the Kodaira dimension of symmetric powers Xm of a complex projective variety X of dimension n ≥ 2 by Arapura and Archava, we study their analytic and algebraic hyperbolic properties. First we show that Xm is special if and only if X is special (except when the core of X is a curve). Then we construct dense entire curves in (suf-ficiently hig) symmetric powers of K3 surfaces and product of curves. We also give a criterion based on the positivity of jet differentials bundles that implies pseudo-hyperbolicity of symmetric powers. As an application, we obtain the Kobayashi hyperbolicity of symmetric powers of generic projective hypersur-faces of sufficiently high degree. On the algebraic side, we give a criterion implying that subvarieties of codimension ≤ n − 2 of symmetric powers are of general type. This applies in particular to varieties with ample cotangent bundles. Finally, based on a metric approach we study symmetric powers of ball quotients.

Hua operators and relative discrete series on line bundle over bounded symmetric domains

Abstract: Let $D=G/K$ be a bounded symmetric domain and $S=K/L$ be its Shilov boundary We consider the action of $G$ with weight $ u\in\mathbb{Z}$ on functions on $D$ viewed as sections the line bundle and the corresponding eigenspace of $G$-invariant di erential operators. The Poisson transform maps hyperfunctions on the $S$ to the eigenspaces. We characterize the image in terms of Hua operators on the sections of the line bundle. For some special parameter the Poisson transform is of Szego type mapping into the relative discrete series; we compute the corresponding elements in the discrete series.