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Séminaire Recherche Opérationnelle - Probabilités et Statistiques

Responsable Ruslan Sadykov

  • Le 10 juin 2024 au 14 juin 2024
  • Manifestations Scientifiques
    Salle de conférences
    Contacts : Luis Fredes - Adrien Richou
    Journées de Probabilités 2024

  • Le 10 juin 2024 à 13:30 au 14 juin 2024 à 12:00
  • Séminaire Images Optimisation et Probabilités
    Salle de conférénces
    Journées de Probabilités 2024

    Page de l'événement : https://indico.math.cnrs.fr/event/11353/overview


  • Le 13 juin 2024 à 14:00
  • Séminaire de Calcul Scientifique et Modélisation
    Salle 2
    Firas Dhaouadi University of Trento
    An Eulerian hyperbolic model for heat transfer derived via Hamilton's principle

    We present a new model for heat transfer in compressible fluid flows. The model is derived from Hamilton’s principle of stationary action in Eulerian coordinates, in a setting where the entropy conservation is recovered as an Euler–Lagrange equation. A sufficient criterion for the hyperbolicity of the model is formulated. The governing equations are asymptotically consistent with the Euler equations for compressible heat conducting fluids, provided the addition of suitable relaxation terms. A study of the Rankine–Hugoniot conditions and Clausius–Duhem inequality is performed for a specific choice of the equation of state. In particular, this reveals that contact discontinuities cannot exist while expansion waves and compression fans are possible solutions to the governing equations. Evidence of these properties is provided on a set of numerical test cases.


  • Le 14 juin 2024 à 09:30
  • Groupe de Travail EDP et Théorie Spectrale
    Salle 1
    Mahdi Zreik (Université de Bordeaux)
    On the self-adjointness of two-dimensional relativistic shell interactions

    In this talk, I will discuss the self-adjointness of the two-dimensional Dirac operator coupled with a singular combination of electrostatic and Lorentz scalar $\delta$-interaction, supported on a closed Lipschitz curve. The main new ingredients are an explicit use of the Cauchy transform on non-smooth curves and a direct link with the Fredholmness of a singular boundary integral operator. This results in a proof of self-adjointness for a new range of coupling constants, which includes and extends all previous results for this class of problems. The study is particularly precise for the case of curvilinear polygons, as the angles can be taken into account in an explicit way. In particular, if the curve is a curvilinear polygon with obtuse angles, then there is a unique self-adjoint realization with domain contained in $H^{1/2}$ for the full range of non-critical coefficients in the transmission condition. The results are based on a joint work with Badreddine Benhellal and Konstantin Pankrashkin.


  • Le 14 juin 2024 à 09:30
  • Séminaire de Géométrie
    Salle 2
    Anja Randecker (Heidelberg)
    The realization problem for Veech groups

    Translation surfaces arise naturally in many different contexts, for example when unfolding billard trajectories or when equipping a Riemann surface with an abelian differential. Most visually, they can be described by (finitely or infinitely many) polygons that are glued along edges which are parallel and have the same length.

    In this talk, we will be interested in the Veech groups of translation surfaces, that is, the stabilizer of the natural GL(2,R) action on the moduli space for a given translation surface. Although Veech groups have been studied for several decades, they are in itself not fully understood yet. In particular, it is not known in general whether a given abstract group can be realized as the Veech group of a translation surface.

    After introducing the realization problem for Veech groups, I will speak about some recent progress in this direction for infinite translation surfaces. This is joint work with Mauro Artigiani, Chandrika Sadanand, Ferrán Valdez, and Gabriela Weitze-Schmithuesen.


  • Le 14 juin 2024 à 11:00
  • Séminaire de Géométrie
    Salle 2
    Vincent Bagayoko (Paris IMJ)
    Ordered groups of regular growth rates

    Certain sets of germs at $+ \infty$ of monotone bijections between neighborhoods of $+ \infty$ form groups under composition. This is the case for germs of functions definable in an o-minimal structure, for certain germs lying in Hardy fields, as well as for more abstract functions defined on fields of formal series, such as transseries. 

    In this talk I will describe properties of the resulting ordered groups, and show that they can be studied using valuation-theoretic tools adapted to this non-commutative context.


  • Le 14 juin 2024 à 14:00
  • Séminaire de Théorie des Nombres
    Salle de conférences
    Salim Rostam (Université de Tours)
    Cocktail à base de partition

    Une partition d'un entier n est une suite décroissante d'entiers positifs de somme n. Cette définition est étroitement liée au groupe symétrique et à sa théorie des représentations. Notamment, pour étudier les représentations sur un corps de caractéristique p on peut utiliser le procédé de p-régularisation, introduit par James, qui à une partition associe une partition p-régulière, c'est-à-dire une partition dont aucune part ne se répète p fois ou plus.Une mesure de probabilité classique sur l'ensemble des partitions de n est la mesure de Plancherel. Un résultat spectaculaire de Kerov–Vershik et Logan–Shepp (1977) donne une forme limite asymptotique pour les grandes partitions tirées selon la mesure de Plancherel. Dans cet exposé, nous montrerons ce que devient ce résultat pour la p-régularisation de grandes partitions. Notamment, il y a toujours existence d'une forme limite, qui est donnée par le « secouage » (shaking) de la courbe de Kerov-Vershik-Logan-Shepp.


  • Le 17 juin 2024 à 14:00
  • Groupe de Travail Analyse
    Salle de conférences
    Bernhard Haak IMB
    Le calcul fonctionnel Besov de Gomilko et Tomilov

  • Le 17 juin 2024 à 14:00 au 21 juin 2024 à 14:00
  • Manifestations Scientifiques
    Bilbao
    Comité d’organisation : Jean-Bernard Bru - Laurent Michel
    Kinetic equation, Mathematical Physics and Probability

  • Le 18 juin 2024 à 11:00
  • Séminaire de Théorie Algorithmique des Nombres
    salle 2
    Eric Ahlqvist University of Edinburgh
    Massey products and class field towers

    I will present recent joint work with Magnus Carlson, where we provide formulas for 3-fold Massey products in the étale cohomology of the ring of integers of a number field. Using these formulas, we identify the first known examples of imaginary quadratic fields with a class group of p-rank two possessing an infinite p-class field tower, where p is an odd prime. Furthermore, we establish a necessary and sufficient condition, in terms of class groups of p-extensions, for the vanishing of 3-fold Massey products. As a consequence, we offer an elementary and sufficient condition for the infinitude of class field towers of imaginary quadratic fields. Additionally, we disprove McLeman’s (3,3)-conjecture.


  • Le 19 juin 2024 à 17:00
  • Séminaire des doctorant·es
    Salle de Conférences
    Mathias Truel IMB
    Non linear reduced order models applied to instationary aeroelastic simulations

    Reduced order models (ROMs) are parametric mathematical models derived from PDEs using previously computed solutions. In many applications, the solution space turns out to be low dimensional, so that one can trade a minimal loss of accuracy for speed and scalability of the numerical model. ROMs counteract the curse of dimensionality by significantly reducing the computational complexity. Overall, reduced order models have reached a certain level of maturity in the last decade, allowing their implementation in large-scale industrial codes, mainly in structural mechanics. Nevertheless, some hard points remain. Parametric problems governed by advection fields or solutions with a substantial compact support such as shock waves suffer from a limited possibility of dimensional reduction and, at the same time, from an insufficient generalization of the model (out-of-sample solutions). The main reason is that the solution space is usually approximated by an affine or linear representation. In this thesis, we aim to contribute to the use of non-intrusive model reduction methods by working on three axes: (i) Application to unsteady computations with non-intrusive interpolation methods; (ii) Use of hybrid models linking reduced models and numerical simulation models with a domain decomposition type approach; (iii) Application to complex industrial problems The flutter problem on a fin will be used as a first complex application case. Indeed, this fluid-structure problem presents very different behaviors according to the flow regimes and is very expensive to simulate without simplifying assumptions. Thus, a hybrid model could accelerate the computation time while remaining accurate in the complex areas. This CIFRE thesis financed by Ingeliance is part of the chaire PROVE financed by ONERA and the Nouvelle Aquitaine region.


  • Le 20 juin 2024 à 11:00
  • Séminaire d'Analyse
    Salle 1 (Attention, salles et horaires exceptionnels)
    Veronica Beltrami Parma
    Navigating Higher-Dimensional Holomorphic Dynamics

    Holomorphic dynamics studies the evolution of complex manifolds under the iteration of holomorphic maps.

    While significant progress has been made in understanding the theory of one-dimensional holomorphic dynamics, the transition to higher dimensions still presents difficult challenges since the situation is vastly different from the one-dimensional case.

    Even only the study of the dynamics of automorphisms (i.e. holomorphic maps injective and surjective) in two dimensions already poses deep difficulties, and the construction of significant examples is an active area of research.

    In this talk, we provide an overview of the dynamics in several complex variables, focusing particularly on the stable dynamics of automorphisms of C^2. We introduce concepts such as Fatou sets, polynomial and transcendental Hénon maps, and limit functions. Finally, we address two recently resolved questions that refer to the current state of my research  (a joint work with A. M. Benini and A. Saracco):

    Can limit sets for (non-recurrent) Fatou components be hyperbolic?

    Can limit sets be distinct?


  • Le 20 juin 2024 à 14:00
  • Séminaire de Calcul Scientifique et Modélisation
    Salle 2
    Dmitri Kuzmin Université de Dortmund
    .

  • Le 21 juin 2024 à 14:00
  • Séminaire de Théorie des Nombres
    Salle de conférences
    Lena Ji (University of Michigan)
    On rationality of real conic bundle threefolds

    For threefolds over the complex numbers, much is understood about the rationality problem, i.e. the property of being birational to projective space. However, much less is known over fields that are not algebraically closed. For example, a threefold defined over the real numbers could become rational after base changing to C, but in general, the complex rationality construction may not descend to R. In this talk, we study this question for real threefolds with a conic bundle structure. This talk is based on joint work with S. Frei, S. Sankar, B. Viray, and I. Vogt, and joint work with M. Ji.


  • Le 24 juin 2024 à 14:00
  • Groupe de Travail Analyse
    Salle de conférences
    Bernhard Haak IMB
    Le calcul fonctionnel Besov de Gomilko et Tomilov

  • Le 25 juin 2024 à 11:00
  • Séminaire de Théorie Algorithmique des Nombres
    salle 2
    Maria Corte-Real Santos University College London
    TBA

  • Le 25 juin 2024 à 11:00
  • Séminaire de Physique Mathématique - EDP
    Salle de conférences
    Chérif Amrouche U. Pau
    Dirichlet problem for the Laplacian and the Bilaplacian in Lipschitz Domains


    We are interested here in questions related to the maximal regularity of solutions of elliptic problems div $(A abla\, u) = f$ in $\Omega$ with Dirichlet boundary condition. For the last 40 years, many works have been concerned with questions when $A$ is a matrix or a function and when $\Omega$ is a Lipschitz domain. Some of them contain incorrect results that are corrected in the present work.


    We give here new proofs and some complements for the case of the Laplacian, the Bilaplacian and the operator $\mathrm{div}\, (A abla)$, when ${\bf A}$ is a matrix or a function. And we extend this study to obtain other regularity results for domains having an adequate regularity. We give also new results for the {Dirichlet-to-Neumann operator for Laplacian and Bilaplacian.


    Using the duality method, we can then revisit the work of Lions-Magenes, concerning the so-called very weak solutions, when the data are less regular.

    Thanks to the interpolation theory, it permits us to extend the classes of solutions and then to obtain new results of regularity.


  • Le 27 juin 2024 à 14:00
  • Séminaire de Calcul Scientifique et Modélisation
    Salle 2
    Davide Torlo SISSA Trieste
    Structure preserving methods via Global Flux quadrature: divergence-free preservation with continuous Finite Element
    In many problems, the emergence of physical structures and equilibrium solutions, such as divergence-free solutions in contexts like shallow water and magneto-hydrodynamics, poses a significant challenge. A simple linear approximation of such systems that already show these behavior is the linear acoustic system of equations. We focus on Cartesian grid discretizations of such system in 2 dimensions and in the preservation of stationary solutions that arise due to a truly multidimensional balance of terms, which corresponds to the divergence-free solutions for acoustic systems.
    Conventional methods, like the continuous Finite Element SUPG, face limitations in maintaining these structures due to the stabilization techniques employed, which do not effectively vanish when the discrete divergence is zero.
    What we propose is to use the Global Flux procedure, which has proven to be successful in preserving 1-dimensional equilibria [1,2], to define some auxiliary variables guiding a suitable discretization of both the divergence and stabilization operators [3]. This approach enables the natural preservation of divergence-free solutions and more intricate equilibria involving various sources. Moreover, this strategy facilitates the identification of discrete equilibria of the scheme that verify boundary or initial conditions. We use the Deferred Correction time discretization, obtaining explicit arbitrarily high order methods.
    Numerous numerical tests validate the accuracy of our proposed scheme compared to classical approaches. Our method not only excels in preserving (discretely) divergence-free solutions and their perturbations but also maintains the original order of accuracy on smooth solutions.

    [1] Y. Cheng, A. Chertock, M. Herty, A. Kurganov and T. Wu. A new approach for designing moving-water equilibria preserving schemes for the shallow water equations. J. Sci. Comput. 80(1): 538–554, 2019.
    [2] M. Ciallella, D. Torlo and M. Ricchiuto. Arbitrary high order WENO finite volume scheme with flux globalization for moving equilibria preservation. Journal of Scientific Computing, 96(2):53, 2023.
    [3] W. Barsukow, M. Ricchiuto and D. Torlo. Structure preserving methods via Global Flux quadrature: divergence-free preservation with continuous Finite Element. In preparation, 2024.
  • Le 28 juin 2024 à 10:45
  • Séminaire de Géométrie
    Salle 2
    Thai-Hoang Lê (Université du Mississippi)
    A préciser

  • Le 2 juillet 2024 à 09:30
  • Soutenances
    Salle de conférences
    Bianca GOUHTIER IMB
    Titre de la thèse :"Actions rationnelles de schémas en groupes infinitésimaux". Directeur de thèse : Dajano Tossici

  • Le 8 juillet 2024 à 14:00
  • Soutenances
    Salle de conférences
    Chadi SABA IMB
    Titre de la thèse : "Le problème de Littlewood et les séries de Fourier non harmoniques". Directeur de thèse : Karim Kellay. Codirecteur : Philippe Jaming

  • Le 8 juillet 2024 à 15:00
  • Soutenances
    Salle 2
    Haojie HONG IMB
    Titre de la thèse : "Grands diviseurs premiers de suites récurrentes linéaires". Directeur de thèse : Yuri Bilu

  • Le 9 juillet 2024 à 13:30
  • Direction
    Salle de conférences
    Conseil conjoint UFMI - IMB (CL/CS)

    Ordre du jour : PGE 2025

    Il sera également possible d’assister au conseil à distance.


  • Le 10 juillet 2024 à 14:00 au 11 juillet 2024 à 12:00
  • Séminaire Images Optimisation et Probabilités
    Salle de conférences
    5 speakers À preciser
    Workshop

    Wednesday 10/07 14h00 Jurgen Angst (Univ. Rennes)

    Title :  TLC in total variation for beta-ensembles

    Résumé : In this talk, we study the fluctuations of linear statistics associated with beta-ensembles, which are statistical physics models generalizing random matrix spectra. In the context of random matrices precisely (e.g. GOE, GUE), the "law of large numbers" is Wigner's theorem, which states that the empirical measure of eigenvalues converges to the semicircle law, and fluctuations around equilibrium can be shown to be Gaussian. We will describe how this result generalizes to beta-ensembles and how it is possible to quantify the speed of convergence to the normal distribution. We obtain optimal rates of convergence for the total variation distance and the Wasserstein distances. To do this, we introduce a variant of Stein's method for a generator $L$ that is not necessarily invertible, and which allows us to establish the asymptotic normality of observables that are not in the image of $L$. Time permitting, we will also look at the phenomenon of super-convergence, which ensures that convergence to the normal law takes place for very strong metrics, typically the $C^{\infty}$-convergence of densities. The talk is based on recent works with R. Herry, D. Malicet and G. Poly.

    Jeudi 11/07 11h00 Simon Coste (Univ. de Paris)



  • Le 11 juillet 2024 à 14:00
  • Séminaire Images Optimisation et Probabilités
    Salle de conférences
    Magalie Benefice IMB
    Soutenance de Thèse

    À preciser


  • Le 11 juillet 2024 à 14:00
  • Soutenances
    Salle de conférences
    Magalie BENEFICE IMB
    Titre de la thèse :"Couplages de processus stochastiques en géométrie sous-riemannienne". Directeur de thèse : Michel Bonnefont. Codirecteur : Marc Arnaudon

  • Le 19 septembre 2024 à 15:30
  • Le Colloquium
    Salle de Conférences
    Virginie Ehrlacher (CERMICS École des Ponts ParisTech)
    TBA

  • Le 24 octobre 2024 à 15:30
  • Le Colloquium
    Salle de Conférénces
    Jose A. Carrillo (Oxford)
    TBA
    TBA