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We discuss the computational problem of finding pairs of consecutive smooth integers, also known as smooth twins. Such twins have had some relevance in isogeny-based cryptography and reducing the smoothness bound of these twins aids the performance of these cryptosystems. However searching for such twins with a small smoothness bound is the most challenging aspect of this problem especially since the set of smooth twins with a fixed smoothness bound is finite. This talk presents new large smooth twins which have a smaller smoothness bound compared to twins found with prior approaches.

L'ordre du jour sera le suivant :

1) Adoption du Compte-Rendu du conseil du 11 juin (vote)

2) Informations générales

3) Plan de Gestion des Emplois des enseignants-chercheurs 2025

4) Questions diverses

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.

15h00 Nicolas Juillet (Univ. Haute-Alsace)

Title :  Exact interpolation of 1-marginals

Résumé : I shall present a new type of martingales that exactly interpolates any given family of 1-dimensional marginals on R1 (satisfying the suitable necessary assumption). The construction makes use of ideas from the (martingale) optimal transportation theory and relies on different stochastic orders. I shall discuss of related constructions and open questions (joint work with Brückerhoff and Huesmann).

16h00 Kolehe Coulibaly-Pasquier (Inst. Ellie Cartan)

Title :  

Résumé :

Jeudi 11/07

10h00 Masha Gordina (Univ. of Connecticut)

11h00 Simon Coste (Univ. de Paris)

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