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En français :

Le but de cet exposé est d’expliciter les liens entre les propriétés analytiques de la fonction zêta de Riemann et la répartition des nombres premiers. Nous examinerons en particulier les conséquences du produit eulérien et de l’influence des zéros non triviaux, aussi bien sur les résultats asymptotiques que sur les formules exactes.

In english:

The aim of this talk is to make explicit the links between the analytic properties of the Riemann zeta function and the distribution of prime numbers. In particular, we will examine the consequences of the Euler product and the influence of the nontrivial zeros, both on asymptotic results and on explicit formulas.

This talk presents computational and theoretical advances/experiments in Mixed Integer Nonlinear Programming across two complementary themes. The first focuses on emerging MINLP techniques — online learning for pseudo cost estimation, ReLU-based neural methods for cut separation, and AlphaEvolve-style modelling — that aim to modernize the MINLP solver. The second focuses on aggregation-based cutting planes, highlighting the practical importance of Complemented Mixed Integer Rounding (CMIR) cuts in modern MILP solvers. A sparsity-driven aggregation framework is introduced that models aggregation as an MILP and a two-stage LP heuristic that produces sparse, strong aggregated rows with measurable gains on MIPLIB2017. Theoretical results show CMIR cuts frequently define faces (and empirically facets) of the convex hull; Fenchel-style normalization is proposed to strengthen them. Finally, we give a prospect on the MINLP solving.

I will first discuss a problem of high-dimensional probability known as the ellipsoid fitting conjecture. I will present recent progress on this conjecture using both non-rigorous analytical tools of statistical physics, and rigorous methods based on the combination of universality results in statistics and extensions of classical approaches in random convex geometry. In a second part, I will discuss how the techniques developed to analyze ellipsoid fitting can be used to sharply characterize optimal learning in a wide neural network with a quadratic activation function, as well as in a model of learning from long sequences of high-dimensional tokens. 

This talk concerns the numerical approximations of a class of linear dispersive Initial Boundary Value Problems (IBVP) which describe the wave propagation in dispersive media. The considered class of IBVP is defined by assumptions on the symmetrization and on the boundary conditions. Under these assumptions, a reformulation of the IBVP with non-local conservation laws will be established. This reformulation will lead to H^1 estimates for the solutions of the dispersive IBVP. A numerical strategy will be proposed to enforce a fully discrete version of such estimates and numerical experiments will be done to assess its relevancy.

Nous discuterons le résultat suivant. Supposons que l’on dispose de deux familles d’applications de Hénon $(f_t)_t$ et $(g_t)_t$, paramétrées par une courbe algébrique, définies sur un corps de nombres, et que l’une d’entre elles soit dissipative. Alors il existe une constante positive $C$ et deux entiers strictement positive $N$ et $M$ telles que, pour tout paramètre $t$, soit le nombre de points périodiques communs à $f_t$ et $g_t$ est inférieur à $C$, soit, $f_t^N = g_t^M$. C'est un travail en cours, en collaboration avec Marc Abboud.

Le résumé de l'exposé de Damien

The half-line Dirac operators with $L^2$-potentials can be characterized by their spectral data. It is known that the spectral correspondence is a homeomorphism: close potentials give rise to close spectral data and vice versa. We prove the first explicit two-sided uniform estimate related to this continuity in the general $L^2$-case. The proof is based on an exact solution of the inverse spectral problem for Dirac operators with $\delta$-interactions on a half-lattice in terms of the Schur's algorithm for analytic functions. The new approach rises interesting questions that I will also discuss in the talk. Joint work with Pavel Gubkin.

I will present a new first-order hyperbolic reformulation of the Cahn-Hilliard equation. The model is obtained from the combination of augmented Lagrangian techniques, with a classical Cattaneo-type relaxation that allows to reformulate diffusion equations as augmented first order hyperbolic systems with stiff relaxation source terms. The proposed system is proven to be hyperbolic and to admit a Lyapunov functional, in accordance with the original equations. A new numerical scheme is proposed to solve the original Cahn-Hilliard equations based on conservative semi-implicit finite differences, while the hyperbolic system was numerically solved by means of a second order MUSCL-Hancock finite volume scheme. The proposed approach is validated through a set of classical benchmarks such as spinodal decomposition, Ostwald ripening and exact stationary solutions.

On lance un dé et la personne choisie improvise un exposé en 15 minutes.

Suivi d'un repas d'équipe à la passerelle.

If $A/k$ is an abelian variety, there are no non trivial maps (linear, bilinear, quadratic) from $A$ (or $A \times B$) to $G_m$. However, seeing these objects as fppf sheafs of anima (i.e., $\infty$-groupoids) rather than fppf sheafs of sets, the space/anima of linear maps, bilinear and quadratic maps is highly non trivial. Using the Dold-Kan correspondance, we can interpret their $\pi_1$ as, respectively:

- linear maps $A \to BG_m$, i.e. as elements of the dual abelian variety $\widehat{A}=Hom(A, BG_m)$

- biextensions of $A \times B$ by $G_m$

- cubical structures on $G_m$-torsors on $A$

This talk will be divided in three part.

In the first elementary part, we will sketch the many analogies between bilinear and quadratic maps on one hand, and polarisations and line bundles on an abelian variety on the other hand.

In the second part, we will give a sketch of the animation procedure and why it explains the above analogies.

Finally, in the third part, we will give algorithmic applications. In particular, cubical arithmetic serves as a swiss-knife toolbox for abelian varieties, since it can be used to recover the biextension arithmetic and theta group arithmetic, and allows to compute pairings, isogenies, radical isogenies, isogeny preimages, change of level... If time permits, we'll also give an example on how it sheds new lights on the DLP, notably via the monodromy leak attack.

La mécanique quantique a 100 ans cette année. Elle a, pendant toutes ces années, alimenté de multiples sources de belles mathématiques. Une telle source est la question toujours d’actualité : ``Mais en quoi donc est-elle si différente de la mécanique classique ?’’ Dans cet exposé nous illustrerons un aspect de cette interrogation : l’utilisation de quasi-probabilités (Wigner, Kirkwood-Dirac, ...) pour (tenter de) capter la frontière classique-quantique. 

L'ordre du jour sera le suivant :

1. Approbation du compte rendu de la réunion du conseil scientifique du 18/11.

2. Examen et classement des demandes de contrats doctoraux fléchés de l'EDMI

3. Discussion autour de la politique scientifique de l'IMB, en particulier concernant les aspects numériques (dans le contexte d'une demande émanant du VP numérique et transmise par le département SIN à tous les labos le constituant).

4. Informations de la direction.

5. Questions diverses.

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We will examine stochastic implicit algorithms. These algorithms have proven more robust with respect to step size selection compared to their explicit counterparts. Specifically, we will show that variance reduction techniques enable to improve the convergence rates of these implicit algorithms as already seen for explicit ones

Séminaire commun avec Optimal

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Attention-based models, such as Transformer, excel across

various tasks but lack a comprehensive theoretical understanding. To

address this gap, we introduce the single-location regression task,

where only one token in a sequence determines the output, and its

position is a latent random variable, retrievable via a linear

projection of the input. To solve this task, we propose a dedicated

predictor, which turns out to be a simplified version of a non-linear

self-attention layer. We study its theoretical properties, both in terms

of statistics (gap to Bayes optimality) and optimization (convergence of

gradient descent). In particular, despite the non-convex nature of the

problem, the predictor effectively learns the underlying structure. This

highlights the capacity of attention mechanisms to handle sparse token

information. Based on Marion et al., Attention Layers Provably Solve

Single-Location Regression, ICLR 2025, and Duranthon et al., Statistical

Advantage of Softmax Attention: Insights from Single-Location

Regression, submitted.

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We study the Vehicle Routing Problem with Stochastic Demands (VRPSD), which involves optimizing delivery routes for vehicles with limited capacity to serve customers whose demands are unknown when designing the routes. The routes are designed taking into account the possibility that a route may have too much demand for the capacity of a vehicle to be delivered, in that case recourse actions can be taken, inducing a cost. This problem seeks to minimize routing costs and the expected recourse costs.

The Vehicle Routing Problem with Stochastic Demands is relevant as it addresses the need for efficient logistics under uncertainty in transportation and supply chain management. As a result, research on this problem is very active, and recent advances in exact resolution methods allow for tackling larger instances more efficiently and with greater generality regarding the different hypotheses surrounding recourse and uncertainty modeling.

In this talk, we present the state-of-the-art methods for solving the VRPSD. We first provide a definition of the problem and list its various components that can vary, such as recourse actions and different ways to model uncertainty. Then, we present different methods from the literature to solve the VRPSD, with a focus on the Disaggregated L-shaped method.