Tous les événements à venir

Un automorphisme parabolique d'une variété hyperkähler est, essentiellement, un automorphisme préservant une fibration lagrangienne. On peut montrer que, quitte à prendre une puissance, il agit par translations sur les fibres. Avec Verbitsky nous avons montre il y a quelques années que les orbites sont denses dans les fibres assez générales. Je parlerai d'un énoncé plus précis (travail en commun avec Serge Cantat): le rang de " l'application de Betti " correspondante est maximale; ainsi que de quelques questions reliées.

The study on multiple zeta values has been actively studied since the 1990s. Several different types of (generalized) multiple zeta functions have been introduced and studied by many researchers. 

In this talk, we introduce a q-generalization of finite version of multiple zeta values. Many relations have been established by several researchers. But, we are interested in explicit formulas at roots of unity, where we can see the forms of polynomials with rational numbers.  On the other hand, the classical Stirling numbers (of the first kind and of the second kind) have been widely studied and generalized in various fields, in particular, in combinatorics. In this talk, we show how certain kinds of generalized Stirling number are closely connected with finite version of multiple zeta values.  

Le résumé de l'exposé de Guillaume

In this talk, I will present several control problems for which the adjoint system is not observable. Although the theory states that controllability is lost in such cases, we may still have weaker notions of controllability. We will present such property in two different contexts, one related to the wave equation based on a joint work with Belhassen Dehman and Enrique Zuazua in which we managed to prove regional controllability, and another one on the heat equation, which is well-known to be approximately controllable. In this latter case, the question is thus to estimate the cost of approximate controllability, a question linked to the density property of the reachable space within the underlying state space.

I will talk about the hydrostatic approximation of the 2d Euler-Boussinesq system, describing the evolution of an inviscid stratified fluid where the vertical length scale is much smaller than the horizontal one. Even though meaningful in oceanography, the justification of the hydrostatic limit in this context has remained an open problem.

I will discuss some recent results showing that some instability mechanisms may prevent this limit to hold. Along the way, I will also draw some connections with large-time issues for stratified fluids and with kinetic theory for plasmas.

We present results concerning the security of post-quantum multivariate signature schemes based on UOV, in particular those submitted to NIST.

We motivate our approach by a geometric interpretation of the trapdoor, based on the work of Kipnis and Shamir and more recently by Beullens.

The geometric properties we exhibit are naturally translated into algebraic problems, which can be solved using standard algebraic cryptanalysis tools,

such as efficient linear algebra and Gröbner basis algorithms.

As an example, we show that the varieties defined by the public keys of UOV schemes admit large singular locii.

These singularities enable us to introduce new algebraic attacks against UOV-based schemes, and to re-interpret the Kipnis-Shamir attack in an algebraic framework.

Our attacks lower the security of UOV\hp and VOX showing in particular that the parameters sets proposed for these schemes do not meet the NIST security requirements.

At level V, we show that the security falls short by a factor of $2^{29}$ logical gates.

We also present on-going work with S. Abelard and M. Safey el Din enabling a generic analysis of the polynomial systems arising in the study of UOV.

Les algorithmes quantiques sont une piste majeure d'accélération pour certains calculs. Dans cet exposé, nous présenterons les principaux problèmes susceptibles d'en bénéficier. Nous développerons également quelques grands principes sous-jacents à ces algorithmes.

(Travaux en commun avec E. Shinder) Nous commençons par rappeler la notion d’application birationnelle entre variétés algébriques et par présenter quelques questions naturelles concernant les groupes de Cremona. Nous introduisons ensuite des invariants de nature motivique associés aux applications birationnelles, que nous utilisons pour démontrer la non-simplicité de la plupart des groupes de Cremona en exhibant des sous-groupes normaux propres. 

Étant donné une courbe elliptique $E/Q$ et un nombre premier $p$, peut-on déterminer toutes les courbes elliptiques $F/Q$ telles que $E[p](Qbar)$ et $F[p](Qbar)$ soient des modules galoisiens isomorphes (on dit alors que $E$ et $F$ sont congrues modulo $p$)? Une conjecture attribuée à Frey et Mazur affirme que lorsque $E$ est fixée et $p$ est assez grand, les seules solutions $F/Q$ sont des courbes elliptiques isogènes à $E$. On peut reformuler ce problème comme la détermination des points rationnels d'une courbe $X_E(p)$, tordue de la courbe modulaire classique $X(p)$ ; une stratégie introduite par Mazur permet d'attaquer ce type de questions. Je présenterai cette stratégie et comment l'appliquer au ces des congruences modulo $23$ à la courbe elliptique $y^2=x^3-23$. 

This talk is devoted to studying propagation phenomena in reaction diffusion and integro-differential equations with a weakly degenerate non-linearity. The reaction terms cover the standard weak Allee effect one and an intermediate between the classical logistic (or Fisher-KPP) non-linearity and the standard weak Allee effect one. We study the effect of the tails of the dispersal kernel on the rate of expansion. When the tail of the kernel is sub-exponential, the exact separation between existence and nonexistence of travelling waves is exhibited. This, in turn, provides the exact separation between finite speed propagation and acceleration in the Cauchy problem. Moreover, the exact rates of acceleration for dispersal kernels with sub-exponential and algebraic tails are provided. Our approach is generic and covers a large variety of dispersal kernels including those leading to convolution and fractional Laplace operators. Numerical simulations are provided to illustrate our results. This comes from joint works with Jérôme Coville, Guillaume Legendre, and Xi Zhang.

To assess the efficacy of a vaccine strategy, there is a need to analyze data harvested during clinical trial in which numerous subjects are followed at several time-points after vaccination via the measurement of biological quantities of interest. For their predictive ability and interpretability, mechanistic models (i.e based on ordinary differential equations) are suited for these tasks. However, they need to be constructed and their parameter estimated first. In this presentation, we will give a brief introduction to such models as well as the existing estimation methods suited for them.

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Le résumé de l'exposé de Léo

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Journée scientifique IA mult-disciplinaire du département SIN

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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.

À préciser

A définir

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.

A définir

À préciser

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..).

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Le résumé de l'exposé d'Elena

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.  

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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Le résumé de l'exposé de Baptiste

suivi d'un repas d'équipe

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À préciser