IMB > Informations générales > Agendas

La semaine de l’IMB

  • Le 19 mars 2024 à 11:00
  • Séminaire de Théorie Algorithmique des Nombres
    salle 2
    Rocco Mora CISPA
    A new approach based on quadratic forms to attack the McEliece cryptosystem
    In this talk, I will present a novel algebraic approach for attacking the McEliece cryptosystem which is currently at the 4-th round of the NIST post-quantum standardization process. The contributions are twofold.
    (1) A new distinguisher on alternant and Goppa codes working in a much broader range of parameters than previous distinguishers is introduced and its complexity analysed;
    (2) With this approach, a polynomial-time key recovery attack on alternant and Goppa codes of high-rate and under some conditions on their field size and degree is also provided.
  • Le 19 mars 2024 à 11:00
  • Séminaire de Physique Mathématique - EDP
    Salle de conférence
    Shu Nakamura Gakushuin University\, Tokyo
    Topics on the essential self-adjointness for Klein-Gordon type operators on spacetimes
    We discuss recent results on the essential self-adjointness of Klein-Gordon type operators on several classes of spacetimes. The first one is the asymptotically flat spacetime, which was studied previously by A. Vasy (J. Spectral Theory 2020) and by us (Ann. H. Lebesgue 2021), but we present a new simpler proof (Ann. H. Poincaré
    2023). We also discuss the essential self-adjointness for the asymptotically static spacetime, which is Cauchy compact (Comm. Math. Phys. 2023). These results are joint work with Kouichi Taira (Ritsumeikan University).
  • Le 20 mars 2024 à 17:00
  • Le séminaire des doctorant·es
    Salle de conférences
    Mounir Hayani IMB
    Prime Number Races
    Chebyshev's bias is the phenomenon stating that the number of prime numbers $p \leq x$ that are congruent to a non-square $a \mod q$, denoted $\pi(x;q,a)$, has strong tendency for these to to be larger than those congruent to a square $b \mod q$, $\pi(x;q,b)$. This bias was quantitatively proven by Rubinstein and Sarnak, in 1994, under some hypotheses, including the Generalized Riemann Hypothesis. In our talk, we will explore their results and extend the discussion to the equivalent concept of Chebyshev's bias in Number Fields.
  • Le 21 mars 2024 à 11:00
  • Séminaire Images Optimisation et Probabilités
    Salle de conférénces.
    Laura Girometti et Léo Portales Université de Bologne et de Toulouse
    Deux exposés
    Title Léo : Convergence of the iterates of Lloyd's algorithm
    Summary : The finding of a discrete measure that approaches a target density, called quantization, is an important aspect of machine learning and is usually done using Lloyd’s algorithm; a continuous counterpart to the K-means algorithm. We have studied two variants of this algorithm: one where we specify the former measure to be uniform (uniform quantization) and one where the weights associated to each point is adjusted to fit the target density (optimal quantization). In either case it is not yet known in the literature whether the iterates of these algorithms converge simply. We proved so with the assumption that the target density is analytic and restricted to a semi algebraic compact and convex set. We do so using tools from o-minimal geometry as well as the Kurdyka-Lojasiewicz inequality. We also proved along the way the definability in an o-minimal structure of functions of the form Y := (y1, ..., yN ) → D(\mu,1/N sum_{i=1}^N \delta_{y_i}) for the following divergences D: the general Wp Wasserstein distance, the max-sliced Wasserstein distance and the entropic regularized Wasserstein distance.

    Title Laura : Quaternary Image Decomposition
    Summary : Decomposing an image into meaningful components is a challenging inverse problem in image processing and has been widely applied to cartooning, texture removal, denoising, soft shadow/spotlight removal, detail enhancement etc. All the valuable contributions to this problem rely on a variational-based formulation where the intrinsic difficulty comes from the numerical intractability of the considered norms, from the tuning of the numerous model parameters, and, overall, from the complexity of extracting noise from a textured image, given the strong similarity between these two components. In this talk, I will present a two-stage variational model for the additive decomposition of images into piecewise constant, smooth, textured and white noise components, focusing on the regularization parameter selection and presenting numerical results of decomposition of textured images corrupted by several kinds of additive white noises.
  • Le 21 mars 2024 à 14:00
  • Séminaire d'Analyse
    Salle de conférences
    Michael Hartz Saarland
    von Neumann's inequality on the polydisc
    The classical von Neumann inequality shows that for any contraction T on a Hilbert space, the operator norm of $p(T)$ satisfies
    $ \|p(T)\| \le \sup_{|z| \le 1} |p(z)|. $
    Whereas Ando extended this inequality to pairs of commuting contractions, the corresponding statement for triples of commuting contractions is false.
    However, it is still not known whether von Neumann's inequality for triples of commuting contractions holds up to a constant. I will talk about this question and about function theoretic upper bounds for $\|p(T)\|$.
  • Le 21 mars 2024 à 14:00
  • Séminaire de Calcul Scientifique et Modélisation
    Salle 2
    Mathieu Rigal IMB
    [Séminaire CSM] Boundary conditions for the Boussinesq-Abbott model with varying bottom
    In the littoral area, mechanisms behind the formation of extreme waves remain poorly understood despite their great socio-economic impact. In order to model these phenomena, it is especially important to take into account nonlinear and dispersive effects, which makes the Boussinesq-Abbott model a pertinent choice. However the presence of high order derivatives impedes the good handling of boundary conditions, which is crucial if one wishes to generate and evacuate waves from the computational domain. In order to raise this difficulty, an equivalent reformulation of this model has recently been proposed in the literature for the case of a flat bottom. This rewriting consists to get rid of the dispersive operator in exchange of a nonlocal flux and a dispersive boundary layer, and allows to efficiently prescribe the elevation of the free surface at the borders of the domain.
    The goal of this work is to extend this approach to the case of a varying bottom, while allowing to enforce more general boundary conditions. Once the nonlocal formulation of the model is established, numerical schemes of order 1 and 2 are proposed and validated through numerical experiments. The impact of different boundary conditions on the solutions is also investigated.
  • Le 22 mars 2024 à 10:45
  • Séminaire de Géométrie
    Salle 2
    Suzanne Schlich (Grenoble)
    Représentations de Bowditch et primitives-stables dans les espaces hyperboliques
    Dans cet exposé, on va introduire les représentations de Bowditch du groupe libre de rang deux (introduites par Bowditch en 1998) ainsi que les représentations primitives-stables (introduites par Minsky en 2010) à valeurs dans les groupes d'isométries d'espaces Gromov-hyperboliques. Minsky a initialement introduit les représentations primitives-stables dans PSL(2,C) afin de construire un domaine ouvert de discontinuité de la variété des caractères. Nous discuterons l'équivalence entre les représentations de Bowditch et les primitives-stables. Nous introduirons également les représentations simples-stables d'un groupe de surface et donnerons un résultat similaire dans le cas de la sphère à quatre trous.
  • Le 22 mars 2024 à 14:00
  • Séminaire de Théorie des Nombres
    Salle de conférences
    Cédric Pilatte (Oxford University)
    Bornes améliorées pour les corrélations logarithmique de fonctions multiplicatives
    La fonction de Liouville $\lambda(n)$ est définie comme étant égale à $+1$ si $n$ est un produit d'un nombre pair de nombres premiers, et à $-1$ dans le cas contraire. Le comportement statistique de $\lambda$ est étroitement lié à la distribution des nombres premiers. À bien des égards, la fonction de Liouville est supposée se comporter comme une séquence aléatoire de $+1$ et de $-1$. Par exemple, la conjecture de Chowla (binaire) prédit que la moyenne de $\lambda(n)\lambda(n+1)$ pour $n < x$ tend vers zéro lorsque $x$ tend vers l'infini. Dans cet exposé, je discuterai des bornes quantitatives pour une version logarithmique de ce problème.
  • Le 25 mars 2024 à 14:00
  • Groupe de Travail Analyse
    Salle de conférences
    Michel Bonnefont IMB
    Couplages stochastiques et décroissance de la distance en variation totale pour la loi de mouvements Browniens sous elliptiques sur le groupe de Heisenberg et les groupes de Carnot.
    Partie 2

    Travail en commun avec Marc Arnaudon, Magalie Bénéfice et Delphine Féral.
  • Le 26 mars 2024 à 11:00
  • Séminaire de Théorie Algorithmique des Nombres
    salle 2
    Bastien Pacifico LIRMM
    From Chudnovsky-type algorithms to locally recoverable codes
    Chudnovsky's method makes it possible to construct multiplication algorithms in finite fields with good bilinear complexity, i.e. a small number of bilinear multiplications in the base field. However, their total complexity and the difficulty of efficiently constructing these algorithms are unfavorable.

    Historically, these are evaluation/interpolation algorithms using rational points of algebraic curves/rational places of function fields. Using asymptotically optimal towers, the existence of algorithms with bilinear complexity that is linear in the degree of extension has been proven. But these algorithms are not constructible in polynomial time.
    Another approach is a recursive construction using places of increasing degrees. It provides algorithms with a quasi-linear bilinear complexity, but constructible in polynomial time.

    We will introduce a hybrid construction, taking the best of both strategies to obtain algorithms with linear bilinear complexity that can be constructed in polynomial time.

    Secondly, we will see that some locally recoverable codes, where the recovery of a corrupted symbol is possible using a small amount of other symbols, appear naturally in the recursive construction of Chudnovsky-type algorithms. We will define and study these codes.

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