Institut de Mathématiques de Marseille, UMR 7373




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13 mars 2018: 4 événements

Séminaire

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  • Séminaire Géométrie Complexe

    Mardi 13 mars 11:00-12:00 - Mattia GALEOTTI - IMJ, Paris

    Moduli of curves with principal and spin bundles : the singular locus via graph theory

    Résumé : In a series of recent papers, Chiodo, Farkas and Ludwig carried out a
    deep analysis of the singular locus of the moduli space of stable (twisted) curves
    with an $\ell$-torsion line bundle. They showed that for $\ell\leq 6$ and $\ell\neq 5$
    pluricanonical forms extend over any desingularization.
    This opens the way to a computation of the Kodaira dimension without desingularizing,
    as done by Farkas and Ludwig for $\ell=2$,
    and by Chiodo, Eisenbud, Farkas and Schreyer
    for $\ell=3$.
    We can generalize this works in two directions.
    At first we treat roots of line bundles on the universal curve systematically :
    we consider the moduli space of curves
    $C$ with a line bundle $L$ such that $L^\xx\ell\cong\omega_C^\xx k$.
    New loci of canonical and non-canonical singularities appear
    for any $k\not\in\ell\Z$ and $\ell>2$, we provide a set of combinatorial tools allowing us
    to completely describe the singular locus in terms of dual graphs.
    Furthermore, we treat moduli spaces of curves with a $G$-cover
    where $G$ is any finite group. In particular for $G=S_3$ we approach
    the evaluation of the Kodaira dimension of the moduli space, and list
    the remaining obstacles to calculate it.

    Lieu : CMI, salle C003 - I2M - Château-Gombert
    39 rue Frédéric Joliot-Curie
    13453 Marseille cedex 13

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  • Séminaire Dynamique, Arithmétique, Combinatoire (Ernest)

    Mardi 13 mars 11:00-12:00 - Adrien RICHARD - I3S, Université de Sophia-Antipolis

    Fixing monotone boolean networks asynchronously

    Résumé : A monotone boolean network with n components is a directed graph on [n]≔1,…,n where each vertex is labeled by a binary variable and a local transition function, which is monotone, boolean and whose inputs are the binary variables of the in-neighbors. An asynchronous run consists in updating vertices, one at each step, by applying its local transition function. Thus a run can be described by the sequence of vertices to update, that is, a word on the alphabet [n]. We prove that there exists a word W on [n] of cubic length such that, for every monotone network with n components, and for every initial configuration, the run described by W leads to a fixed configuration. We also prove that any word with this property is at least of quadratic length. To construct W, we use the following basic result about n-complete words : there is a word of quadratic length containing, as subsequences, all the permutations of [n]. For the lower-bound, we prove the following : there exists a subexponential set of permutations of [n] such that every word containing all these permutations as subsequences is of quadratic length.
    This is a joint work with Julio Aracena, Maximilien Gadouleau and Lilian Salinas. A preprint is available here : https://arxiv.org/abs/1802.02068.

    Lieu : Salle des séminaires 304-306 (3ème étage) - Institut de Mathématiques de Marseille (UMR 7373)
    Site Sud - Bâtiment TPR2
    Campus de Luminy, Case 907
    13288 MARSEILLE Cedex 9

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  • Séminaire Analyse Appliquée (AA)

    Mardi 13 mars 11:00-12:00 - Weiwei DING - Meiji University

    Dynamics of time-periodic reaction-diffusion equations with compact initial support on R

    Résumé : This work is concerned with the asymptotic behavior of bounded solutions of the Cauchy problem
    u_t=u_{xx} +f(t,u), \qquad  x\in \mathbb{R},\,t>0,
    u(x,0)= u_0
    where $u_0$ is a nonnegative bounded function with compact support and $f$ is periodic in $t$ and satisfies $f(\cdot,0)=0$. We first prove that the $\omega$-limit set of any bounded solution either consists of a single time-periodic solution or it consists of time-periodic solutions as well as heteroclinic solutions connecting them. Furthermore, under a minor nondegenerate assumption on time-periodic solutions of the corresponding ODE, the convergence to a time-periodic solution is proved. Lastly, we apply these results to equations with bistable nonlinearity and combustion nonlinearity, and specify more precisely which time-periodic solutions can possibly be selected as the limit.
    This is a joint work with Hiroshi Matano.

    JPEG - 11.4 ko
    Weiwei DING

    Lieu : CMI, salle de séminaire R164 (1er étage) - I2M - Château-Gombert
    39 rue Frédéric Joliot-Curie
    13453 Marseille cedex 13

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  • 13 mars 2018: 1 événement

    groupe de travail

    • Agenda ERC IChaos

      Du 12 au 16 mars - Pierre LAZAG

      Collaboration scientifique avec Nizar DEMNI

      Résumé : Collaboration portant sur l’étude des processus déterminantaux

      Lieu : UFR Mathématiques Rennes

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