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Publié le 24 juillet 2020

Post-Doctorat en statistiques/médecine au LAREMA ouvert en septembre 2020

Models of job-exposure matrices for biomechanical constraints and health effects. Plus de renseignements ici

Publié le 14 décembre 2019

Masterclass : du 17 décembre au 19 décembre 2019

Deux cours : Sinan Yalin : Deformation theory and formal moduli problems Nicolas Raymond : Weyl’s asymptotic law for the Dirichlet Laplacian https://www.lebesgue.fr/fr/content/seminars-masterclass19

Publié le 30 novembre 2019

3 décembre 2019 Cérémonie Doctorat Honoris Causa de Olav Arnfinn LAUDAL

3-12-2019 : Le titre de docteur Hnoris Causa de l’université d’Angers est remis à Olav Arnfinn Laudal (mathématiques) et Martine Hennard Dutheil de la Rochère (Anglais) 4-12-2019 Journée en l’honneur de A. Laudal 10h – O.A. Laudal : Deformations of thick points and mathematical models in science 14h30 – V. Lychagin : Invariants : Differential […]

Publié le 29 mars 2019

Workshop on mixed Hodge modules and Hodge ideals

Réunion annuelle du GDR Singularité et applications, 1-5 Avril 2019 Nero Budur : Hodge ideals Michel Granger : Bernstein polynomials Claude Sabbah : Mixed Hodge module

Publié le 16 août 2018

International Conference on « Advanced Methods in Mathematical Finance »

28-31 August 2018 This conference is dedicated to innovations in the mathematical analysis of financial data, new numerical methods for finance and applications to risk modeling. The selected topics include actuarial theory, risk measures, ruin theory, credit default models, stochastic control and its applications to portfolio choice and liquidation, models of liquidity and with transaction […]

Publié le 15 août 2018

Retakh Fest

Colloque Non-commutative structures, cluster algebras and applications. 25 au 30 juin 2018 Les algèbres amassées introduites par S. Fomin et A. Zelevinsky en 2001 sont des anneaux commutatifs munis de générateurs distingués (variables d’amas), engendrés par une procédure itérative (mutation). Les motivations initiales étaient liées à la théorie de Lie (positivité totale, bases canoniques) et […]

Séminaire des doctorant.es
In this talk, I will give an introductory overview of several ideas arising from the study of random coverings of the circle. I will begin with the classical Dvoretzky covering problem, which asks when a sequence of randomly placed intervals covers the circle infinitely often. I will then introduce a few basic notions from harmonic analysis, especially Fourier coefficients of measures and the concept of Rajchman measures. The main object of the talk will be the Dvoretzky measure, a natural random measure supported on the non-covered set. I will explain why one is interested in proving that this measure has the Rajchman property, and I will present the main intuition behind the proof: instead of estimating Fourier coefficients directly, one studies suitable convolutions of the measure and shows that they become absolutely continuous. Finally, I will briefly introduce the broader framework of multiplicative chaos measures, which provides a useful perspective on the Dvoretzky measure and connects the problem to recent developments in random geometry and harmonic analysis. The talk will be expository and aimed at presenting the main ideas rather than technical details.

Séminaire des doctorant.es
Mon exposé sera une introduction générale à la topologie algébrique, en prenant comme fil rouge la question fondamentale du domaine : comment classifier les espaces à déformation près ? J'introduirai d'abord la notion de (co)homologie, qui fournit les invariants topologiques les plus fondamentaux, et la théorie "d'algèbre linéaire" associé, appelée algèbre homologique, dont les objets de base sont les complexes de (co)chaînes. On verra que pour s'approcher d'une classification des espaces (à déformation près), il est nécessaire de raffiner ces complexes en les munissant de structures algébriques plus riches. On illustrera cette idée avec l'exemple de la structure d'anneau sur la cohomologie. Je terminerai avec quelques mots sur le théorème de Mandell, qui pousse ce principe beaucoup plus loin et fournit une réponse complète au problème de classification, pour une large classe d'espaces. Ainsi, on rencontrera des "structures algébriques à homotopie près" sur les complexes de chaînes, qui sont au cœur de la théorie de l'homotopie moderne. J'essaierai autant que possible d'illustrer les différents concepts par des exemples élémentaires.

Séminaire de topologie et géométrie algébriques
The Gromov-Witten theory gives deformation invariants of a complex variety by counting curves. The generating function of these invariants naturally satisfies some differential equations, which in turn provide intricate information on the derived category of coherent sheaves, or the birational structure. In this talk, I discuss a K-theoretic version, where the invariants are still defined by counting curves but the generating functions naturally satisfy q-difference equations instead. I discuss my work on the generating function of the K-theoretic Gromov-WItten invariants of type-A flag varieties. I also discuss predictions on the q-difference equations by the 3D mirror symmetry, as well as potential applications.

Séminaire de topologie et géométrie algébriques

Séminaire des doctorant.es
Le séminaire des doctorants se propose de fournir aux doctorants une occasion de s'ouvrir aux autres domaines des mathématiques que le leur. A chaque séance, un intervenant réalise un exposé sur un fait standard de leur domaine d'étude, de niveau adapté à l'ensemble des doctorants. Un anneau de polynômes est-il l'ensemble des suites à support fini ou l'ensemble des fonctions polynomiales ? Mon lemme de topologie est vrai dans les espaces métriques, les espaces compacts ou même les groupes topologiques, mais je ne souhaite pas le démontrer plusieurs fois. Je souhaite travailler avec des fonctions méromorphes, et pourtant, j'ai encore du mal à écrire rigoureusement toutes les conditions de la définition. Derrière ces exemples se cache une dure réalité : - Nos preuves sont très vulnérables à une légère modification anodine des pages précédentes. - Nous devons souvent refaire des preuves très similaires en raison d'hypothèses légèrement différentes. - Nos preuves doivent tenir compte de la manière dont nous avons démontré certains lemmes (et pas seulement des lemmes). Ce sont précisément les problèmes que certains paradigmes de programmation nous permettent d'éviter. Cela est particulièrement utile pour expliquer les mathématiques à un assistant de preuve, mais nous verrons que la mise en œuvre de ces paradigmes sur nos trois exemples peut changer la façon dont nous faisons des mathématiques « sur papier ».

Séminaire de probabilités et statistiques
TBA

Séminaire des doctorant.es
Les coefficients dans le développement en série entière de 1/(1-t)^n correspondent aux dimensions des espaces de polynômes homogènes en n variables. Ce phénomène combinatoire reflète la dualité de Koszul entre l'algèbre symétrique S(V) et l'algèbre extérieure \Lambda(V) engendrées par un espace vectoriel V de dimension n. Cette dualité, est à la base d'un complexe de chaînes nommé résolution de Koszul par Priddy à la fin des années 60'. Le cas de l'algèbre symétrique permet de calculer la résolution de Koszul de l'algèbre enveloppante d'une algèbre de Lie, correspondant alors au complexe de Chevalley-Eilenberg calculant la cohomologie d'une algèbre de Lie.

Séminaire de topologie et géométrie algébriques

Séminaires systèmes dynamiques et géométrie
TBA

Séminaire des doctorant.es
In the first part, it focuses on the inference of stable autoregressive processes whose parameters evolve toward an unstable regime. The aim is to bridge the gap between stability and instability and in particular to characterize the asymptotic behaviors of the estimators and their rates of convergence. Consistency and asymptotic normality properties are established for the least squares estimator within this class of nearly-unstable autoregressive processes. This framework is particularly suitable for addressing the unit root problem, resulting in non-stationarity, and has enabled the development of a statistical test designed to assess whether a time series is close, or not, to a non-stationary regime. In the second part, long-memory processes are considered, with the study focusing on model selection within a general class of FARIMA processes driven by weakly white noise, which is uncorrelated but may exhibit very general nonlinear dependencies. The consistency of the BIC and QBIC criteria is established for weak FARIMA processes, including the non-stationary case

Séminaire de topologie et géométrie algébriques
The affine Grassmannian (and its Beilinson-Drinfeld version) for a curve and an algebraic group is a very useful classical tool in geometric representation theory and Geometric Langlands. The situation in higher dimensions is, so far, unexplored. I will propose some geometric versions of affine Grassmannians for surfaces (and an algebraic group), describe them as quotients, and prove representability results. This is a joint work with A. Maffei (Università di Pisa) and V. Melani (Università di Firenze).

Séminaire de probabilités et statistiques
Federated learning on Riemannian manifolds enables collaborative training without centralized data pooling when model parameters are intrinsically constrained. Existing methods either rely on geometric operations lacking closed-form expressions on key manifolds (such as the Stiefel manifold), employ optimizer-specific gradient streams that incur information loss through successive transports, or -- even when computationally cheap -- require drift correction terms and full client participation. We propose two aggregation strategies, RFedProj and RFedRL, that are optimizer-agnostic, lightweight (requiring only standard projections and retractions), and support partial participation without auxiliary correction. Both achieve identical convergence rates under these relaxed conditions and data heterogeneity, with bounds explicitly characterizing how participation ratio and heterogeneity interact -- mirroring classical Euclidean federated guarantees. Experiments on EEG motor imagery classification with SPDNet on compact Stiefel manifolds validate competitive performance against centralized and Euclidean baselines.

Séminaires systèmes dynamiques et géométrie
We study compact locally conformally K\"ahler (lcK) manifolds which are Calabi--Yau, in the sense that $c_1^{BC}(X)=0$. First of all, we prove that all the known lcK manifolds which are Calabi--Yau are Vaisman. Then we prove that an lcK Chern--Ricci flat metric that is Gauduchon is necessarily Vaisman. Finally, specializing to Calabi--Yau solvmanifolds with left-invariant complex structure, we prove that a left-invariant metric is lcK if and only if it is Vaisman. Therefore, they are finite quotients of the Kodaira manifold.

Séminaire de probabilités et statistiques
We consider the framework of least-squares penalized estimation where the penalty term is given by a polyhedral norm, or more generally, a polyhedral gauge, which encompasses methods such as LASSO and. generalized LASSO, SLOPE, OSCAR, PACS and others. Each of these estimators can uncover a different structure or “pattern”of the unknown parameter vector. We define a novel and general notion of patterns based on subdifferentials and formalize an approach to measure pattern complexity. For pattern recovery, we provide a minimal condition for a particular pattern to be detected with positive probability, the so-called accessibility condition. We make the connection to estimation uniqueness by showing that uniqueness holds if and only if no pattern with complexity exceeding the rank of the X-matrix is accessible. Subsequently, we introduce the noiseless recovery condition which is a stronger requirement than accessibility and which can be shown to play exactly the same role as the well-known irrepresentability condition for the LASSO – in that the probability of pattern recovery is bounded by 1/2 if the condition is not satisfied. Through this, we unify and extend the irrepresentability condition to a broad class of penalized estimators using an interpretable criterion. We also look at the “gap” between accessibility and the noiseless recovery condition and discuss that our criteria show that it is more pronounced for simple patterns. Finally, we prove that the noiseless recovery condition can indeed be relaxed when turning to so-called thresholded penalized estimation: in this setting, the accessibility condition is already sucient (and necessary) for sure pattern recovery provided that the signal of the pattern is large enough. We demonstrate how our findings can be interpreted through a geometrical lens throughout the talk and illustrate our results for the Lasso as well as other estimation procedures. Related references: P. Graczyk, U. Schneider, T. Skalski and P. Tardivel, A Unified Framework for Pattern Recovery in Penalized and Thresholded Estimation and its Geometry; https://doi.org/10.1007/s10957-025-02863-6 U. Schneider and P. Tardivel, The Geometry of Uniqueness, Sparsity and Clustering in Penalized Estimation; https://jmlr.org/papers/v23/21-0420.html K. Ewald and U. Schneider, On the Distribution, Model Selection Properties and Uniqueness of the Lasso Estimator in Low and High Dimensions; https://doi.org/10.1214/20-EJS1687

Séminaire des doctorant.es
For the first part, let $\mathbb{K}$ be an algebraically closed field of characteristic zero. Given a nonzero polynomial \[ f = y^n + a_1(\underline{x}) y^{n-1} + \cdots + a_n(\underline{x}) \in \mathbb{K}[x_1, \dots, x_e][y], \] we show how to associate with $f$ an affine semigroup of ${\mathbb N}^e$. The main idea is to associate with $f$, after a preparation result, a quasi-ordinary polynomial. Our results generalize to a global situation, local results obtained by A.Abbas and A. Assi. For the second part, we classify curves with one place at infinity according to the difference between the total Milnor invariant and the total Tjurina invariant. We note that the local classification for the cases where this difference is zero was carried out by Zariski, while the cases corresponding to differences 1 and 2 were studied by Bayer and Hafez, and the case 3 by Watari. Our result provides a global classification in this setting.

Séminaire des doctorant.es
La théorie de Yang--Mills quantique décrit les interactions élémentaires à l’aide d'intégrales sur des espaces de dimension infinie, courbés et peu structurés. La construction rigoureuse de la mesure permettant de donner sens à ces intégrales demeure un défi mathématique majeur. Si aucune construction n’est connue à ce jour dans le cas d’un espace-temps de dimension 3 ou 4, le cas de la dimension 2 a été étudié avec succès par plusieurs auteurs. Dans cet exposé, je présenterai les objets mathématiques impliqués dans l'étude de la mesure de Yang–Mills en deux dimensions, ainsi qu'une contribution récente avec Nguyen Viet Dang.

Séminaire de topologie et géométrie algébriques
Here are seemingly unrelated problems: Koszul duality for the category of a reductive group in representation theory, the existence of a K-contact non-Sasakian manifold in differential geometry, splitting Drinfeld space’s de Rham complex in the p-adic Langlands program, deformation quantization of Poisson manifolds in mathematical physics. And yet, all of them boil down to the same question: formality. A differential graded algebraic structure A (e.g. an associative algebra, a Lie algebra, a pre-Calabi-Yau algebra, etc.) is formal if it is related to its homology H(A) by a zig-zag of quasi-isomorphisms preserving the algebraic structure. The examples mentioned above rely on criteria that guarantee formality. These include formality descent, formality in families, intrinsic formality, domination techniques, the behavior of formality in fibrations, and many others. In this talk, I will prove that all these criteria arise as special cases of a single theorem: formality transmission. On the one hand, this theorem unifies the aforementioned results into a single theory; on the other hand, it generalizes these criteria in diverse directions, in particular over any coefficient ring and for algebraic structures with several outputs: algebras encoded by properads.

Séminaires systèmes dynamiques et géométrie
This is an ongoing joint project with Fuchs, Lima, de Rezende and Silveira. We propose to study the very simple but fundamental question regarding bifurcation theory of critical points: When can an isolated critical point of a smooth function be destroyed by a C^2-small perturbation of the function? Of course, non-vanishing of local Morse homology is an obstruction, and we study whether it is the only obstruction. I will explain why in dimensions two and three local Morse homology is expected to be the only obstruction, and why in dimension four the situation is absolutely unclear.

Séminaire de probabilités et statistiques
Je présenterai une toute nouvelle méthode pour montrer, à partir de 0, le comportement champ moyen de la percolation critique en dimension d>6. L’idée principale est pour p

Séminaire des doctorant.es
After giving a definition of what is a category, I will show that the notion can actually be formulated in categorical terms. Even though this does not help us to define classical categories, we can iterate the construction of categories inside categories themselves. I will present why this is something mathematicians are interested in and classify such internal categories in the category of groups and in the category of abelian groups , which will naturally lead to the notion of crossed modules of groups. References : Internal Crossed Modules. G. Janelidze Combinatorial homotopy II. J.C. Whitehead