A transfer principle: from periods to isoperiodic foliations

In this paper we study the dynamics and topology of the isoperiodic foliation defined on the Hodge bundle over the moduli space of genus $g\geq 2$ curves

The oriented graph of multi-graftings in the Fuchsian case

We prove the connectedness and calculate the diameter of the oriented graph of graftings associated to exotic complex projective structures on a compact surface S with a given holonomy representation of Fuchsian type. The oriented graph of graftings is the graph whose vertices are the equivalence classes of marked CP^1-structures on S with a given fixed holonomy, and there is an oriented edge between two structures if the second is obtained from the first by grafting.Comment: Improved version. The paper chaged title: from "The oriented graph of graftings..." to "The oriented graph of multi-graftings...

Créer des ponts en classe au moyen de la musique

L'auteur de cet article relate les difficultés qu’il a connues avec un groupe d’étudiants fermés à son enseignement et comment son expérience de l'utilisation de la musique dans son cours de philosophie lui a permis de surmonter ce fossé. En s'inspirant d'un aphorisme d'Héraclite indiquant que « le monde est une harmonie de tensions [...] comme celle de la lyre », il a apporté sa mandoline en classe pour illustrer l'idée de contradiction et en a joué quelques notes. Devant la transformation positive de sa relation avec ses étudiants, le professeur se met à utiliser la musique en guise de préambule aux cours, parfois pour illustrer un concept disciplinaire, mais surtout pour créer chez les étudiants une disposition psychologique favorable à l'apprentissage. L'auteur explicite l'impact de la musique sur le plan pédagogique, soulignant notamment que celle-ci peut jouer un rôle déterminant sur la relation entre maître et étudiants en raison de sa grande portée sensitive : elle capte l'attention des étudiants pour créer un état d'esprit positif et renforce la cohésion des groupes. Selon lui, les professeurs ont tout intérêt à ajouter une activité qui tient compte de la dimension affective de l'apprentissage, crée un certain engouement chez les étudiants et ouvre la porte à leur engagement dans le cours

A non-conservative Harris ergodic theorem

We consider non-conservative positive semigroups and obtain necessary and sufficient conditions for uniform exponential contraction in weighted total variation norm. This ensures the existence of Perron eigenelements and provides quantitative estimates of the spectral gap, complementing Krein-Rutman theorems and generalizing probabilistic approaches. The proof is based on a non-homogenous $h$-transform of the semigroup and the construction of Lyapunov functions for this latter. It exploits then the classical necessary and sufficient conditions of Harris's theorem for conservative semigroups and recent techniques developed for the study of absorbed Markov processes. We apply these results to population dynamics. We obtain exponential convergence of birth and death processes conditioned on survival to their quasi-stationary distribution, as well as estimates on exponential relaxation to stationary profiles in growth-fragmentation PDEs

On an irreducibility type condition for the ergodicity of nonconservative semigroups

We propose a simple criterion, inspired from the irreducible aperiodic Markov chains, to derive the exponential convergence of general positive semi-groups. When not checkable on the whole state space, it can be combined to the use of Lyapunov functions. It differs from the usual generalization of irreducibility and is based on the accessibility of the trajectories of the underlying dynamics. It allows to obtain new existence results of principal eigenelements, and their exponential attractiveness, for a nonlocal selection-mutation population dynamics model defined in a space-time varying environment

On an irreducibility type condition for the ergodicity of nonconservative semigroups

We propose a simple criterion, inspired from the irreducible aperiodic Markov chains, to derive the exponential convergence of general positive semigroups. When not checkable on the whole state space, it can be combined to the use of Lyapunov functions. It differs from the usual generalization of irreducibility and is based on the accessibility of the trajectories of the underlying dynamics. It allows to obtain new existence results of principal eigenelements, and their exponential attractiveness, for a nonlocal selection-mutation population dynamics model defined in a space-time varying environment