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Le résumé de l'exposé de Elena

In complex dynamics, one studies the iteration of a holomorphic function, with a special focus on stable and chaotic behavior. Historically, functions from the complex plane to itself have been of particular interest. In this one-dimensional setting, there is an exhaustive characterization of stable components, known as Fatou components. In this talk, I will first give a brief overview of this classification before describing one approach to extending this understanding to higher dimensions, where similar characterizations have remained elusive. Specifically, I focus on skew-products, a simpler family of two-dimensional holomorphic functions.

Cette présentation propose une analyse sociologique des rapports de genre au sein de la licence de mathématiques à l’Université de Bordeaux. À partir d’une enquête ethnographique réalisée dans le cadre d’un mémoire de recherche en sociologie, il s’agit de comprendre comment le genre s’immisce et façonne le quotidien et les trajectoires des étudiantes dans un environnement académique encore largement masculin. Les résultats de cette recherche mettent en lumière les mécanismes (souvent discrets ou invisibles) s’exprimant dans les pratiques, les espaces et les représentations, qui participent à reproduire les inégalités de genre dans les formations scientifiques fondamentales. Cette recherche invite ainsi à réfléchir aux leviers d’action possibles afin de favoriser la mixité et l’égalité dans ces filières.

Les résultats présentés proviennent d'un travail de stage de M2 dirigé par Sophie Duchesne, Christèle Etchegaray et Nicolas Papadakis.

Journée scientifique IA mult-disciplinaire du département SIN

The Klein-Gordon equation is a wave equation with an additional mass damping term. In this presentation, I will review some literature about the dynamic of such equation when settled on an unbounded one-dimensional spatial domain. I will further present some new results regarding the global existence and long time behaviour of solutions that are initialy close to constant or periodic equilibria. Most notably, I will talk about a viscous approximation of this equation, as well as describe how uniformly local orbital stability can be obtained from polar decomposition. This is joint work with Björn de Rijk, Emile Bukieda and Dorothee Frey.

We present an overview of modular polynomial-based proofs of knowledge for isogeny paths. The general recipe encodes each step of an isogeny path via a modular polynomial, which is then translated into a rank-1 constraint system and plugged into a suitable zero-knowledge succinct non-interactive argument of knowledge. This approach was originally introduced by Cong--Lai--Levin (ACNS 2023) using the classical modular polynomial, but other modular polynomials can be used to achieve smaller and more efficient proofs: In joint work with T. den Hollander, S. Kleine, M. Mula and D. Slamanig (CRYPTO 2025) we explored the use of the canonical modular polynomial for significant improvements, and in ongoing follow-up work we found that both the Atkin and Weber modular polynomials yield further improvements. As these three classes of modular polynomials are less prominent than the classical modular polynomial, especially in the context of isogeny-based cryptography, we will briefly explain how they are constructed and will then investigate how they can be used to encode a step of an isogeny path. Finally, we detail the practical improvements obtained from each of these classes.

The cutoff phenomenon occurs in the study of the convergence of ergodic Markov chains towards their invariant measure. For a large class of these objects, we can expect that, when a size parameter (dimension, number of objects) becomes asymptotically large, convergence occurs abruptly. The aim of this presentation is to give an example of a natural Markov chain for which this phenomenon is relatively easy to prove.

After reviewing discrete-time Markov chains, we will present their continuous-time counterparts. We will then define Brownian motion on the torus and see how it fits into this framework. The end of the presentation will be devoted to concluding the proof of the cutoff.

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Le phénomène de cutoff intervient dans l'étude de la convergence des chaines de Markov ergodiques vers leur mesure invariante. Pour une grande catégorie de ces objets, on peut s'attendre à ce que lorsqu'un paramètre de taille (dimension, nombre d'objets) devient asymptotiquement grand, la convergence s'effectue brutalement. L'objectif de cet exposé est de donner un exemple de chaine de Markov naturelle pour laquelle ce phénomène est relativement facile à démontrer.

Après avoir donné quelques rappels sur les chaines de Markov en temps discret, on présentera leur homologue en temps continu. Nous définirons ensuite le mouvement brownien sur le tore et verrons comment il s'inscrit dans ce cadre. La fin de la présentation sera dévolue à conclure la preuve du cutoff.

 I will talk about harmonic maps with respect to non-local 

Dirichlet forms. In particular, I will focus on stochastic processes 

with jumps on manifolds associated with them.

Bilevel optimization is useful in machine learning to tackle problems such as hyperparameter tuning, metalearning or even optimal transport problems. However it presents theoretical and computational challenges, particularly in the nonconvex setting. This talk presents recent advances that may improve our understanding of the complexity, algorithmic strategies, and statistical properties of bilevel problems. We establish the hardness of smooth bilevel programs by showing their equivalence to general lower semicontinuous minimization and proving that polynomial bilevel problems are Σ_p^2-hard (harder than NP-hard). This a joint work with J. Bolte, Q. T. Le & E. Pauwels.

Radio Frequency Integrated Circuits (RFICs) have democratized communications, with ever-greater data exchanges. With each generation, we invent new technologies and systems that increase communication potential by a new order of magnitude: 2G and 3G are nearing their sunset, 4G is fading from our memory, 5G is already in everyone’s pocket, and 6G is rapidly approaching. The future will not only link devices but also bridge human and artificial intelligences. Tomorrow’s networks will rely on integrated circuits we design today, but sustaining the exponential progression demands more than engineering alone. It requires an alliance between technology and science to keep pushing the boundaries of connectivity, ensuring that innovation remains possible in this never-ending race for communication.

In this talk I will present a conjecture of Burnett, which characterizes weak limits of solutions to the Einstein vacuum equations from general relativity. After a brief review of the Cauchy problem for these equations, I will show how their seemingly messy nonlinear structure actually leads to some beautiful cancellations. I will conclude by discussing potential Riemannian versions of Burnett's conjecture, in connection with results by Gromov and Lohkamp.

À préciser

An important challenge in DNA replication analysis is to recover the so-called replication timing profile, that contains important information about the DNA replication dynamics. We show that using recent replication data, this problem can be expressed as a nonlinear inverse problem where the unknown timing profile is assumed to be piecewise affine. 

We propose a novel formalism and computational approach to harness it. In the noiseless case, we establish sufficient identifiability conditions for the timing profile, and prove that it is the solution of a non-convex optimization problem. This problem is specially challenging because of its multiple local minima. We propose the DNA-Inverse optimization method that provably finds the global solution in the noiseless case and is shown to be numerically effective for noisy signals. Besides being more computationally effective than thestate-of-the-art optimization methods, our approach automatically recovers the full configuration of the replication dynamics.This is crucial for DNA replication analysis, and was not possible with previous methods.

Aujourd’hui tout le monde s’accorde sur l’omniprésence de l’Intelligence Artificielle (IA) dans notre quotidien. Cependant, l’IA gérée actuellement par les GAFAM (Google, Amazon, Facebook, Apple et Microsoft) est décentralisée sur des serveurs. Sachant que la consommation électrique de l’Internet représente 5% de la production mondiale (rapport 2023 de l'Agence Internationale de l'Energie) et que le trafic Internet augmente de 25% par an, il faut d’ores et déjà envisager des solutions de calcul alternatives faute de désillusion. Sachant que le cerveau humain consomme 20W, plusieurs équipes dans le monde pensent qu’une solution résiderait dans la réalisation d’architectures neuromorphiques (réseaux de neurones artificiels matériels). De plus les progrès récents des sciences des matériaux ont permis de proposer plusieurs solutions pour réaliser des neurones ou des synapses (memristors, spintronique, isolants de Mott, etc..).

Dans cet exposé nous présenterons un modèle de banquise à l'échelle des floes (blocs de glace) en interaction entre eux mais aussi avec l'océan et l'atmosphère (interaction passive pour ces deux derniers). L'enjeu de l'étude est de construire un outil de calcul suffisamment efficace pour effectuer des simulations à grande échelle (plusieurs milliers de floes) sur des packs (groupes de floes) hétérogènes (taille allant du mètre au kilomètre). Les défis de ce type de modélisation sont multiples, il vont de la gestion des contacts entre floes à la prise en compte des mécanismes de fracturation ou encore de fonte et croissance. Dans cet exposé, nous présenterons dans un premier temps les principes de base adoptés pour la dynamique des floes indéformables et non fracturables (chocs, frottement, drag océanique, forçage par le vent etc.) ainsi que les stratégies de mise en oeuvre numérique (discrétisation du problème, schéma, accélération des calculs via la parallélisation). Dans un second temps, nous nous concentrerons sur l'introduction des mécanismes de fracturation et en particulier la percussion, allant de la construction du modèle utilisé via une étude asymptotique à réduction des temps de simulations grâce au développement d'un noyau de type IA pour le préconditionnement des calculs.

n this talk, we will present recent results on $L^p$-estimates for maximal directional singular integral operators in $\mathbb{R}^n$. These operators are given by a Hörmander–Mihlin multiplier on an $(n-1)$-dimensional subspace and act trivially in the perpendicular direction. The subspace is allowed to depend measurably on the first $n-1$ variables of $\mathbb{R}^n$.

Assuming the subspace is non-degenerate (in the sense that it is away from a cone around $e_n$) and the function $f$ is frequency supported in a cone away from $\mathbb{R}^{n-1}$, we establish $L^p$-bounds for these operators for $p > 3/2$. If we additionally assume that $f$ is frequency supported in a single frequency band, we are able to extend the boundedness range to $p > 1$. We will also discuss why the non-degeneracy assumption cannot in general be removed, even in the band-limited case.

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Le résumé de l'exposé de Léo

In holomorphic dynamical systems, one studies maps on the Riemann sphere (or other complex manifolds) with focus on their Julia sets and invariant measures. From this point of view, the Lattès maps -- those that are quotients of maps on elliptic curves -- are rather uninteresting; their dynamical features are well understood. But viewed algebraically, there are still many unanswered questions. I'll begin the talk with some history of these maps. Then I'll describe a recent question about the geometry of torsion points on elliptic curves and how it has led to interesting complex-dynamical questions about other families of maps and, in turn, new perspectives on the arithmetic side.  

State-Space Models (SSMs) are deterministic or stochastic dynamical systems defined by two processes. The state process, which is not observed directly, models the transformation of the states over time. On another hand, the observation process produces the observables on which model fitting and prediction are based. Ecology frequently uses stochastic SSMs to represent the imperfectly observed dynamics of population sizes or animal movement. However, several simulation-based evaluations of model performance suggest broad identifiability issues in ecological SSMs. Formal SSM identifiability is typically investigated using exhaustive summaries, which are simplified representations of the model. The theory on exhaustive summaries is largely based on continuous-time deterministic modelling and those for ecological SSMs have developed by analogy. While the discreteness of time does not constitute a challenge, finding a good exhaustive summary for a stochastic SSM is more difficult. The strategy adopted so far has been to create exhaustive summaries based on a transfer function of the expectations of the stochastic process. However, this evaluation of identifiability does not allow to take into account the possible dependency between the variance parameters and the process parameters. We show that the output spectral density plays a key role in stochastic SSM identifiability assessment. This allows us to define a new suitable exhaustive summary. Using several ecological examples, we show that usual ecological models are often theoretically identifiable, suggesting that most SSM estimation problems are due to practical rather than theoretical identifiability issues.

Dans ce séminaire, je parlerai de différents schémas d’optimisation stochastique, tels que la descente de gradient stochastique et le schéma de Heavy-Ball stochastique. Nous établirons des estimations d’erreur faible uniformes en temps pour l’erreur entre la solution du schéma numérique et celle d’équations différentielles continues modifiées (ou à haute résolution) aux premier et deuxième ordres, par rapport à la taille du pas de temps. Enfin, nous illustrerons ces résultats par des présentations de simulations numériques.

Aujourd'hui, l'Europe et la France en particulier sont face à des défis de très grande envergure : adaptation aux impacts du changement climatique, positionnement face aux superpuissances (USA, Chine), désindustrialisation, perte de souveraineté, d'attractivité et de compétitivité, etc. Le numérique n'échappe pas à cette situation. Alors, face aux GAFAM et aux BATX, développer des communs numériques ne serait-il pas une réponse adaptée ?

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Updatable Encryption (UE) allows ciphertexts to be updated under new keys without decryption, enabling efficient key rotation. Constructing post-quantum UE with strong security guarantees is challenging: the only known CCA-secure scheme, COM-UE, uses bitwise encryption, resulting in large ciphertexts and high computational costs.

We introduce DINE, a CCA-secure, isogeny-based post-quantum UE scheme that is both compact and efficient. Each encryption, decryption, or update requires only a few power-of-2 isogeny computations in dimension 2 to encrypt 28B messages, yielding 320B ciphertexts and 224B update tokens at NIST security level 1---significantly smaller than prior constructions. Our full C implementation demonstrates practical performances: updates in 7ms, encryptions in 48ms, and decryptions in 86ms.

Our design builds on recent advances in isogeny-based cryptography, combining high-dimensional isogeny representations with the Deuring correspondence. We also introduce new algorithms for the Deuring correspondence which may be of independent interest. Moreover, the security of our scheme relies on new problems that might open interesting perspectives in isogeny-based cryptography.

preprint: https://eprint.iacr.org/2025/1853

À préciser

After a quick overview of the general principles of Life Cycle Assessment (LCA), we will investigate how such a tool can be helpful to compare the environmental impact of different architectures of computer systems used for teaching purposes in higher education. In particular, we will see how to perform the life cycle inventory of the systems under studies from a practical standpoint. We will then review the main results from the life cycle impact assessment and discuss them as well as the limitations of this study.

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Le résumé de l'exposé de Pascal

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Les transports évoluent vers des systèmes toujours plus connectés, capables de répondre à des enjeux majeurs tels que la sécurité, la fluidité du trafic et l’impact environnemental. Les Systèmes de Transport Intelligents Coopératifs (C-ITS) reposent sur la communication en temps réel entre véhicules, infrastructures et usagers, grâce aux avancées en réseaux, capteurs et traitement de données.

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A définir

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suivi d'un repas d'équipe

Lien bientot disponible

Séminaire commun avec Optimal

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 à définir

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