Tous les événements à venir

For an AG code C = C(D, G) on a curve X /Fq , the structure of the hull (the intersection of a code with its dual) plays an important role in code equivalence, entanglement-assisted quantum codes, and efficient decoding. In general the hull need not be an AG code, but it becomes one when a certain divisor A associated to G and its dual divisor H is non-special. This reduces the problem to determining when effective divisors of the form A = \sum_{P in X} \max{v_P(G), v_P(H)} P are non special. In this talk I give explicit criteria for non-speciality of several classes of effective divisors of small degree on Kummer extensions. The characterization is obtained using the description of the Weierstrass semigroup at multiple points of these curves.

These results yield new families where the hull of an AG code can be written again as an AG code, and illustrate how the geometry of Kummer extensions controls the Riemann–Roch behaviour of low-degree divisors.

In this presentation, devoted to the one-dimensional nonlinear Schrödinger equation with non-zero boundary conditions at infinity, we will investigate different notions of stability in order to study certain special solutions known as travelling waves. These solutions appear in the large-time dynamics of general dispersive systems, and we will explain how such solutions, referred to as solitons, are crucial for understanding the overall behavior of solutions to these equations and how they are related to the notion of integrability of the system. Many different behaviors for these travelling waves have been highlighted, according to the shape of the nonlinearity. Nevertheless, we have been able to prove the existence of travelling waves with small momentum. Moreover, we shall dwell on the existence and uniqueness travelling waves with speed close to the speed of sound, the orbital stability of a well-prepared chain of such travelling waves, as well as the asymptotic stability of these special solutions.

English: I will briefly explain what an Algebraic Geometry code (AG code) on surface is, before talking about their duals.

French: Je vais présenter dans les grandes lignes ce qu'est un code de géométrie algébrique (AG), notamment sur les surfaces, et parler de leurs duaux.

Advances in single-cell sequencing have enabled high-dimensional profiling of individual cells, giving rise to single-cell data science and new statistical challenges. A key task is the comparative analysis of single-cell datasets across conditions, tissues, or perturbations, where traditional gene-wise differential expression methods often fail to capture complex, non-linear distributional differences. Perturbation experiments further amplify this challenge by introducing structured, high-dimensional responses that are poorly modeled by linear approaches.

We propose a kernel-based framework for differential analysis of single-cell data that enables non-linear, distribution-level comparisons by embedding data into a reproducing kernel Hilbert space. Our method quantifies differences between cellular populations through distances between mean embeddings and supports formal hypothesis testing in complex experimental designs, including perturbation studies via linear models in RKHS. The approach is robust to high dimensionality, sparsity, and noise, and is implemented in the Python package kaov, which provides visualization and interpretation tools. By offering a flexible, distribution-free alternative to classical methods, kernel-based testing facilitates the detection of subtle but biologically meaningful changes in single-cell data, enabling deeper insights into cellular regulation, disease mechanisms, and precision medicine.

A homogenized model is proposed for linear waves in 1D microstructured media. It combines second-order asymptotic homogenization (to account for dispersion) and interface correctors (for transmission from or towards homogeneous media). A new bound on a second-order effective coefficient is proven, ensuring well-posedness of the homogenized model whatever the microstructure. Based on an analogy with existing enriched continua, the evolution equations are reformulated as a dispersive hyperbolic system. The efficiency of the model is illustrated via time-domain numerical simulations. An extension to Dirac source terms is also proposed.

Time-frequency transforms are powerful signal processing tools. They enable us to analyse signals locally and extract key information, such as frequency or scaling components. The most popular transforms are the short-time Fourier transform (STFT) and the continuous wavelet transform (CWT). However, one issue with these transforms is that they have a fixed resolution; the time-frequency resolution is fully determined by the window function or the mother wavelet, regardless of the properties of the analysed signal. This can lead to a lack of precision when signals move from highly contained transient parts to highly contained harmonic parts, depending on the size of the window. This presentation introduces a solution to this problem: adaptive time-frequency transforms based on modifying the window function according to the analysed signal. We refer to this behaviour as the 'focus phenomenon' and it is linked to objects called 'focus functions'. We will define the adaptive transforms and introduce fundamental results such as the frame theorem, stability estimates, and focus function construction. We will also provide a few examples of applications of these transforms for audio processing.

Dans cet exposé, je donnerai un aperçu de la relation entre les géométries lorentziennes à courbure constante et la théorie de Teichmüller, un sujet initié par l'article fondateur de Geoffrey Mess en 1990. Dans cet esprit, je présenterai des résultats récents établissant une correspondance entre des champs de vecteurs sur le plan hyperbolique et des surfaces de type espace dans l'espace co-Minkowski, également appelé espace "half-pipe".

À l'aide de cette construction, j'étudierai le problème d'extension de champs de vecteurs définis sur le cercle au plan hyperbolique. Nous montrons que tout champ de vecteurs sur le cercle s'étend en un champ de vecteurs harmonique lagrangien sur le plan hyperbolique. J'expliquerai ensuite comment les propriétés de ces champs de vecteurs peuvent être interprétées en termes de géométrie des surfaces associées dans l'espace co-Minkowski, ainsi que du comportement de leurs bords asymptotiques.

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Le résumé de l'exposé de Henri

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In this talk, we will present a fictitious domain finite element method called Phi-FEM, well suited for elliptic problems posed in a domain given by a level-set function without requiring a mesh fitting the boundary. Unlike other recent fictitious domain-type methods (XFEM, Cut-FEM), our approach does not need any non-standard numerical integration, neither on the cut mesh elements nor on the actual boundary. We shall present the proofs of optimal convergence of our methods on the example of Poisson equation using Lagrange finite elements of any order. We will also give numerical tests illustrating the optimal convergence of our methods and discuss the conditioning of resulting linear systems and the robustness with respect to the geometry. We highlight the flexibility and efficiency of our method on elastic and dynamic problems. And more recently, we propose a Phi-FEM formulation to solve particulate flows and Stokes equations.

L’objectif de cet exposé est de mettre en lumière le lien entre la dynamique holomorphe, les équations fonctionnelles et la théorie des opérateurs, à travers l’étude spectrale des opérateurs de composition pondérés $W_{m,\phi}$ sur l’espace $Hol(\Omega)$ des fonctions holomorphes sur le disque et la boule unité de dimension $N$. En effet, le comportement du spectre ponctuel, et les outils utilisés pour le déterminer, dépendent fortement de la nature du symbole $\phi$ (hyperbolique, parabolique ou elliptique), ainsi que de la valeur du poids $m$ au point fixe de $\phi$. Ce travail est en collaboration avec Frédéric Bayart.

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We consider the motion of an inextensible hanging string of finite length under the action of the gravity. The motion is governed by nonlinear and nonlocal hyperbolic equations, which is degenerate at the free end of the string. We report that the initial boundary value problem to the equations of motion is well-posed locally in time in weighted Sobolev spaces at the quasilinear regularity threshold under a stability condition. This is a joint work with Masahiro Takayama at Keio University.

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Pl@ntNet is a global citizen science platform that harnesses artificial intelligence to enable large-scale plant species identification and biodiversity monitoring.

With millions of contributors across over 200 countries, it represents one of the world’s largest biodiversity observatories.

While such platforms offer a cost-effective and scalable approach to data collection, the quality of user-generated annotations can vary significantly.

This variability can affect the reliability of automated plant identification, which is a key issue for both research and real-world biodiversity monitoring applications.

To address these challenges, we propose robust aggregation techniques to consolidate training data and reduce biases stemming from heterogeneous contributor inputs.

We further leverage statistically grounded prediction methods, including conformal prediction, to provide valid confidence sets for species identification, specifically optimized for long-tail classification scenarios.

La dynamique linéaire s’intéresse à l’évolution des itérations d’un opérateur linéaire borné agissant sur un espace de Banach ou de Fréchet. Malgré la simplicité apparente du cadre linéaire, ce type de systèmes peut présenter des comportements très riches, voire inattendus. Un résultat important en ce sens est le critère de Godefroy–Shapiro, qui relie l’abondance de vecteurs propres à l’existence d’orbites denses. Dans cet exposé, je me concentrerai sur les opérateurs de Toeplitz sur l’espace de Hardy et expliquerai comment leur comportement dynamique est rélié à des propriétés géométriques de leur symbole.

Nous expliquons l’importance de l’estimation d’une moyenne de série singulière dans l’étude de la répartition des nombres premiers dans les petits intervalles.

Suivant la conjecture d’Hardy et Littlewood, elle nous permet d’estimer le moment de certaines sommes sur les nombres premiers. Nous expliquons ensuite les idées nouvelles de 

 la méthode mise en place pour améliorer les résultats de Montgomery et Soundararajan et Kuperberg sur ces sommes de séries singulières relatives à trois nombres premiers.

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Public-Key Pseudorandom Correlation Functions (PK-PCFs) are functions that generate pseudorandom correlated strings. These correlations can then be used to speed up secure computation protocols. Recent works have made significant progress building PK-PCFs using group-based assumptions, however, these assumptions do not hold up against quantum attackers. Much less is known about PK-PCFs in the post-quantum regime. In this talk, I will introduce an efficient lattice-based PK-PCF for oblivious transfer (OT) correlations. At the heart of our result lie several technical contributions that might be of independent interest. In particular, we introduce the first efficient lattice-based constrained pseudorandom functions for low-degree polynomials, from a new but natural “secret-power” variant of ring learning with errors (ring LWE) assumption.

À préciser

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A définir

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A flag is a sequence of nested linear subspaces of increasing dimension. It can also be defined as a sequence of mutually-orthogonal subspaces, whose dimensions form the type. The set of flags of the same type forms a smooth, compact and connected Riemannian manifold. As abstract as these flag manifolds may seem, this talk aims to demonstrate that they are truly important in statistics.

The eigenspaces of a real symmetric matrix form a flag, whose type corresponds to the multiplicities of the eigenvalues. Consequently, flag manifolds should naturally be involved in certain essential statistical methods such as principal component analysis, which is based precisely on the spectral decomposition of the empirical covariance matrix. However, their use in statistics remains very limited, in favor of simpler spaces such as Stiefel and Grassmann manifolds, to which the principal components and subspaces used in dimension reduction belong, respectively.

A first fundamental contribution of this talk is the discovery of a new type of parsimony in covariance matrices. Our study of flag manifolds reveals that the number of covariance parameters decreases quadratically with the multiplicities of the eigenvalues. By virtue of the principle of parsimony, we show that empirical eigenvalues whose relative distance is below a certain threshold should be equalized. This result has an important impact in statistics: it implies a transition from principal component analysis to principal subspace analysis, with clear gains in interpretability.

Several extensions of our principal subspace analysis are proposed. In particular, we reformulate the choice of flag type as an optimization problem on the space of covariance matrices, stratified by the multiplicities of the eigenvalues. A lasso-like relaxation on the eigenvalues drastically improves the speed of model selection. Other methodologies—such as hierarchical clustering of eigenvalues and Bayesian approximation of marginal likelihood—are also explored.

In order to improve expressiveness, we extend our principal subspace analysis to mixture models. Since learning parameters via a classic expectation–maximization algorithm makes model selection difficult, we propose a variant that automatically estimates and groups eigenvalues. We obtain theoretical guarantees on the monotonicity of the objective function during iterations, which makes our approach promising for learning parsimonious mixture models.

Finally, we show that certain dimensionality reduction methods suffer from a problem: the representations they produce at different dimensions are not nested. Extending our methodology via a simple and generic principle—involving optimization on flag manifolds—allows us to naturally obtain consistent representations.

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A définir

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https://cgbordeaux.sciencesconf.org/

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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.

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Ce workshop vise à rassembler la communauté mathématique s’intéressant au domaine de l’intelligence artificielle. L’objectif de ce workshop et de permettre le maximum d’échanges scientifiques entre les chercheurs s’intéressants aux différents aspects de l’IA.

L’essor des méthodes basées sur l’apprentissage machine et l’intelligence artificielle dans de nombreux domaines a ammené de nouveaux besoins d’analyse mathématiques des dites méthodes. En effet, la modélisation mathématique en IA permet d’aborder de manière rigoureuse les questions d’explicabilité, d’efficacité et de sécurité des outils basés sur l’IA. D’un point de vue mathématique, de nombreuses disciplines classiques sont concernées par les problématiques issues de l’IA, offrant souvent des angles nouveaux et transverses d’études.

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.