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X-ORIGINAL-URL:https://www.math.ens.psl.eu
X-WR-CALDESC:évènements pour Département de mathématiques et applications
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TZID:Europe/Paris
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:20260329T010000
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DTSTART:20261025T010000
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260407T093000
DTEND;TZID=Europe/Paris:20260407T123000
DTSTAMP:20260518T233349
CREATED:20251018T115430Z
LAST-MODIFIED:20260326T185638Z
UID:20142-1775554200-1775565000@www.math.ens.psl.eu
SUMMARY:Computer-Assisted Proofs of 3D Euler Singularity and Nonuniqueness of Leray–Hopf Solutions for the Unforced 3D Navier–Stokes Equations
DESCRIPTION:Speaker: Thomas Hou (Caltech) \n\n\n\nThe talk will take place in « Amphithéâtre Galois »\, underground near the math library\, 45 rue d’Ulm\, Paris \n\n\n\nWhether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data remains one of the central open problems in nonlinear PDEs. In this talk\, I will present recent joint work with Dr. Jiajie Chen\, in which we rigorously prove finite-time blowup for the 2D Boussinesq equations and the 3D axisymmetric Euler equations with smooth initial data and smooth boundary. Our approach uses a dynamically rescaled formulation that reduces singularity formation to the long-time stability of an approximate self-similar blowup profile. A key difficulty is proving the linear stability of a numerically constructed profile. To address this\, we decompose the solution operator into a leading-order part\, which admits sharp stability estimates\, and a finite-rank perturbation\, which is controlled by a computer-assisted proof. I will also discuss recent joint work with Yixuan Wang and Changhe Yang on nonuniqueness of Leray–Hopf solutions to the unforced 3D incompressible Navier–Stokes equations. In this setting\, the viscous term introduces several new ingredients but also greatly simplifies the analysis: standard $H^1$ estimates suffice\, without the singular weights needed in the inviscid case. A central step is to establish the existence of a self-similar Leray–Hopf solution and then prove the existence of a second solution by analyzing the stability of the linearized operator around this profile and showing that it admits an unstable mode. These results highlight the fruitful interplay among analysis\, computation\, and rigorous validation in nonlinear PDEs.
URL:https://www.math.ens.psl.eu/evenement/thomas-hou/
LOCATION:ENS — amphi Galois\, 45 rue d'Ulm\, Paris\, France
CATEGORIES:Séminaire Analyse non linéaire et EDP
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260408T093000
DTEND;TZID=Europe/Paris:20260408T103000
DTSTAMP:20260518T233349
CREATED:20260403T083819Z
LAST-MODIFIED:20260403T083820Z
UID:21217-1775640600-1775644200@www.math.ens.psl.eu
SUMMARY:Brisures de symétrie\, distributions et double quotients
DESCRIPTION:Soit G′ ⊂ G une paire de groupes et (V\, π) une représentation de G. Les problèmes de branchements consistent à étudier le comportement de la restriction π|G′ de π à G′. Dans le cas où V est un espace de Hilbert\, π est unitaire et G\, G′ sont localement compacts (par exemple des groupes de Lie)\, un théorème de Mautner implique que π|G′ se décompose (de manière unique si G′ est de type I) en intégrale directe de représentations irréductibles de G′. Lorsque π n’est pas unitaire (par exemple si π est une représentation lisse d’un groupe de Lie)\, une telle décomposition en irréductibles n’existe pas. Dans ce contexte plus général\, l’étude de π|G′ peut se faire à travers les espaces d’opérateurs de brisure de symétrie\, c’est-à-dire les espaces Hom_G′(π\, τ) où τ parcourt une classe appropriée de représentations de G. Dans le cas où G et G′ sont des groupes de Lie réductifs réels (par exemple (G\, G′) = (GL(n+1\, R)\, GL(n\, R)))\, une classe de représentations raisonnable de G et G′ est donnée par les représentations de leur série principale\, représentations obtenues par induction parabolique et donc géométriquement à partir de fibrés vectoriels homogènes. Dans cet exposé\, nous verrons à travers des exemples comment et pourquoi les distributions\, couplées à un certain double quotient\, fournissent un angle d’attaque redoutable pour l’étude des problèmes de branchement des groupes de Lie réductifs réels. \n\n\n\n.
URL:https://www.math.ens.psl.eu/evenement/brisures-de-symetrie-distributions-et-double-quotients/
LOCATION:Salle W
CATEGORIES:Colloquium doctorant
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260408T110000
DTEND;TZID=Europe/Paris:20260408T120000
DTSTAMP:20260518T233349
CREATED:20260402T124328Z
LAST-MODIFIED:20260402T124444Z
UID:21211-1775646000-1775649600@www.math.ens.psl.eu
SUMMARY:Basile Morando\, raconte-nous les groupes de Neretin !
DESCRIPTION:Les groupes de Neretin ont été définis par Yuri Neretin au début des années 90\, à l’origine comme analogues p-adiques du groupe des difféomorphismes du cercle. Depuis la preuve de leur simplicité par Kapoudjian en 1999\, ces groupes (localement compacts et totalement discontinus) suscitent un intérêt croissant: ils présentent de remarquables propriétés qui contrastent avec celles des groupes localement compacts simples connexes. Dans cet exposé\, on s’intéressera notamment au fait qu’ils n’admettent aucun réseau\, ainsi qu’aux propriétés remarquables de leurs représentations unitaires.
URL:https://www.math.ens.psl.eu/evenement/basile-morando-raconte-nous-les-groupes-de-neretin/
LOCATION:Salle W toits du DMA
CATEGORIES:Algèbre et géométrie,Séminaire Raconte-moi
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260408T140000
DTEND;TZID=Europe/Paris:20260408T170000
DTSTAMP:20260518T233349
CREATED:20260403T082003Z
LAST-MODIFIED:20260403T082112Z
UID:21215-1775656800-1775667600@www.math.ens.psl.eu
SUMMARY:Un après-midi de théorie des groupes - Adrien Boyer\, Julien Marché\, Greg Patchell
DESCRIPTION:14:00-14:45 Adrien Boyer (IMJ-PRG): Property RD and Boundary Representations for A2 Buildings  \n\n\n\n15:00-15:45 Julien Marché (ENS – PSL): Action of endomorphisms of free groups on their SL_2-character varieties  \n\n\n\n16:15-17:00 Greg Patchell (University of Oxford): Selfless Inclusions of C*-Algebras and Quantum Groups \n\n\n\n \n\n\n\nAbstracts: \n\n\n\nGreg Patchell: Selfless Inclusions of C*-Algebras and Quantum Groups \n\n\n\nRecently\, strong asymptotic freeness\, or selflessness\, in C-algebras has emerged as a powerful technique to prove important regularity properties including simplicity\, unique trace\, stable rank 1\, and strict comparison. In particular\, in Fall 2024\, Amrutam\, Gao\, Kunnwalkam Elayavalli\, and I showed that the reduced group C-algebras of all hyperbolic groups with trivial finite radical are selfless\, which resolved the open problem of strict comparison for the reduced group C-algebra of the free group on two generators. Since then\, our result has been expanded to include a much larger class of groups. Work has also begun on isolating selflessness for C-algebras not arising from groups\, including the result of Hayes\, Kunnawalkam Elayavalli\, and Robert on selflessness of the reduced free product of a large class of C-algebras (see also Flores-Klisse-Ó Cobhthaigh-Pagliero). I will introduce the general notion of a selfless inclusion of C-algebras\, with which we will see the selflessness of the reduced unitary compact matrix quantum groups. This work is joint with Ben Hayes\, Srivatsav Kunnawalkam Elayavalli\, and Leonel Robert. \n\n\n\n \n\n\n\nAdrien Boyer: Property RD and Boundary Representations for A2 Buildings \n\n\n\nI will discuss an approach based on boundary representations to prove property RD for discrete groups acting properly and cocompactly on affine buildings of type A2. This result is due to Robertson\, Ramagge\, and Steger in the late 1990s. I will emphasize geometric arguments involving the Furstenberg boundary that can be used to establish property RD\, in particular the notion of “foldings” or “confluences\,” as suggested by V. Kaimanovich. Along the way\, I will also mention a conjecture of Robertson\, Ramagge\, and Steger concerning the optimal bound\, and propose a possible approach toward resolving it. If time permits\, I will also explain what happens in the C2 case. This is joint work with Thang Nguyen. \n\n\n\n \n\n\n\nJulien Marché: Action of endomorphisms of free groups on their SL_2-character varieties. \n\n\n\nLet phi : F_n->F_n be an endomorphism and let phi^* denote its action on the character variety X_n=Hom(F_n\,SL_2(C))/SL_2(C). Cantat-Gelander-Souto raised the question whether phi^* is an automorphism of the affine variety X_n if and only if phi is an automorphism of F_n. I will describe work in progress which relates directly this question to the action of endomorphisms on the outer space CV_n through a compactification of X_n with special valuations.
URL:https://www.math.ens.psl.eu/evenement/un-apres-midi-de-theorie-des-groupes-adrien-boyer-julien-marche-greg-patchell/
LOCATION:Salle W
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260409T124500
DTEND;TZID=Europe/Paris:20260409T134500
DTSTAMP:20260518T233349
CREATED:20260326T102406Z
LAST-MODIFIED:20260326T102534Z
UID:21172-1775738700-1775742300@www.math.ens.psl.eu
SUMMARY:ENS-Data Science colloquium - Michael Chertkov : Samples That Cooperate\, Samples That Remember: Two Exactly Solvable Bridge Diffusions
DESCRIPTION:Diffusion-based generative models treat samples as independent and memoryless. I will show that relaxing each assumption leads to rich\, exactly solvable physics — with no neural networks anywhere.Giving samples a present — coupling them through their evolving mean field — produces a McKean–Vlasov optimal transport problem whose self-consistent guidance is provably the linear interpolant between endpoint means\, for arbitrary distributions and any interaction schedule; applied to building-fleet demand response\, this saves 20%+ in actuation energy.Giving samples a past produces a continual-learning agent whose memory is a Bridge Diffusion and whose forgetting — arising from a single lossy temporal coarse-graining step — obeys a universal linear capacity law with a Shannon-like constant.Both constructions live in the world of Riccati equations\, hyperbolic functions\, and mixture linear algebra; the physics of the bridge — not the expressivity of a network — controls what is achievable. \n\n\n\n  \n\n\n\nThese seminars are being made possible through the support of the CFM-ENS Chair « Modèles et Sciences des Données ». \n\n\n\nThe organizers: Giulio Biroli\, Alex Cayco Gajic\, Bruno Loureiro\, Stéphane Mallat\, Gabriel Peyré.
URL:https://www.math.ens.psl.eu/evenement/ens-data-science-colloquium-michael-chertkov-samples-that-cooperate-samples-that-remember-two-exactly-solvable-bridge-diffusions/
LOCATION:ENS Salle Dussane
CATEGORIES:ENS-Data Science colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260413T110000
DTEND;TZID=Europe/Paris:20260413T120000
DTSTAMP:20260518T233349
CREATED:20260407T123429Z
LAST-MODIFIED:20260407T124734Z
UID:21247-1776078000-1776081600@www.math.ens.psl.eu
SUMMARY:Serte Donderwinkel - Counting connected graphs
DESCRIPTION:How many connected graphs have a prescribed degree sequence?This classical combinatorial question turns out to admit a natural probabilistic approach. \nIn joint ongoing work with Sasha Bell and Remco van der Hofstad\, we derive asymptotic formulas for the number of connected graphs with a given degree sequence. Our approach is an example of the probabilistic method: rather than counting directly\, we introduce a suitable random graph model and study the likelihood that it exhibits a desired structure. \nConcretely\, we construct a random graph in which (an approximation of) the prescribed degree sequence appears with high probability inside a large connected component. This perspective allows us to translate questions about enumeration into probabilistic statements about random graphs. \nAlong the way\, I will discuss several key probabilistic tools\, including the configuration model\, branching process approximations\, and local weak convergence\, and explain how they combine to yield asymptotic counting results.
URL:https://www.math.ens.psl.eu/evenement/serte-donderwinkel-counting-connected-graphs/
LOCATION:Salle W (ENS)
CATEGORIES:Séminaire informel de probabilités
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260415T110000
DTEND;TZID=Europe/Paris:20260415T120000
DTSTAMP:20260518T233349
CREATED:20260410T085407Z
LAST-MODIFIED:20260410T085408Z
UID:21253-1776250800-1776254400@www.math.ens.psl.eu
SUMMARY:Conformal Prediction for Uncertainty Quantification in Machine Learning: Recent Advances
DESCRIPTION:Machine learning models are often seen as black-box systems that output point predictions without indicating how confident they are in those predictions. Recently\, Conformal Prediction (CP) has emerged as a powerful framework to address this issue by transforming point predictions into set-valued predictions with probabilistic guarantees. In this talk\, I will introduce CP and briefly present some key challenges and recent advances in the area. I will first discuss how to perform CP in a Federated Learning setting\, showing that a single round of communication is sufficient to match the performance of centralized approaches. I will then turn to the question of efficiency control in CP\, where finite-sample guarantees can be obtained by viewing CP as a minimum-volume set estimation problem. \n\n\n\nThis talk is based on the following papers:  \n\n\n\nP. Humbert\, B. Le Bars\, A. Bellet\, S. Arlot. One-Shot Federated Conformal Prediction\, ICML 2023 \n\n\n\nP. Humbert\, B. Le Bars\, A. Bellet\, S. Arlot. Marginal and Training-Conditional Guarantees in One-Shot Federated Conformal Prediction\, Arxiv preprint 2024 \n\n\n\nB. Le Bars\, P. Humbert. On Volume Minimization in Conformal Regression\, ICML 2025
URL:https://www.math.ens.psl.eu/evenement/conformal-prediction-for-uncertainty-quantification-in-machine-learning-recent-advances/
LOCATION:Salle W
CATEGORIES:CSD seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260420T160000
DTEND;TZID=Europe/Paris:20260420T170000
DTSTAMP:20260518T233349
CREATED:20260420T084734Z
LAST-MODIFIED:20260421T074741Z
UID:21313-1776700800-1776704400@www.math.ens.psl.eu
SUMMARY:Gaspar Gomez - Trois exemples élémentaires de renormalisation
DESCRIPTION:La renormalisation est un concept flou\, qui provient de la physique théorique et qui est aujourd’hui abondamment étudié en mathématiques. La renormalisation peut être déroutante: il peut par exemple s’agir de retirer des quantités infinies dans des équations pour qu’elles soient bien posées. N’étant pas un spécialiste de la question\, je ne vous présenterai pas une approche générale mais plutôt trois exemples très élémentaires\, qui je l’espère\, vous rendront familier de ce concept et surtout le démystifieront. Le premier est déterministe\, il s’agit de la distribution valeur principale. Le second est probabiliste : ce sont les processus stables qui généralisent le mouvement brownien. Selon le temps\, je vous parlerai ensuite d’un troisième exemple: l’équation de la chaleur stochastique avec bruit multiplicatif. \n\n\n\n.
URL:https://www.math.ens.psl.eu/evenement/mael-laoufi-trois-exemples-elementaires-de-renormalisation/
LOCATION:Salle W
CATEGORIES:Colloquium doctorant
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260422T131500
DTEND;TZID=Europe/Paris:20260422T141500
DTSTAMP:20260518T233349
CREATED:20260401T122700Z
LAST-MODIFIED:20260505T151040Z
UID:21201-1776863700-1776867300@www.math.ens.psl.eu
SUMMARY:Flots géodésiques\, à l’intersection entre géométrie\, topologie et dynamique
DESCRIPTION:Une métrique riemannienne sur une variété différentielle est un objet qui permet de mesurer des volumes\, et en particulier la longueur des courbes. Les courbes qui localement\, en un certain sens\, minimisent cette longueur sont appelées géodésiques. L’ensemble de ces courbes admet une caractérisation dynamique par un flot défini sur l’espace total du fibré tangent de la variété : le flot géodésique. Cette classe de systèmes dynamiques est parmi les plus célèbres : elle peut être considérée comme un modèle simplifié pour les systèmes hamiltoniens issus de la mécanique céleste\, et en même temps elle a inspiré le développement de plusieurs sujets en topologie et en dynamique\, notamment la théorie de Morse et la dynamique symplectique. Dans cet exposé\, je vais introduire les flots géodésiques\, et je ferai une promenade à travers l’histoire du sujet\, surtout pour les aspects concernant les orbites périodiques. \n\n\n\n\n\n\n\nSéminaires des Mathématiques
URL:https://www.math.ens.psl.eu/evenement/marco-mazzucchelli/
LOCATION:ENS — amphi Galois\, 45 rue d'Ulm\, Paris\, France
CATEGORIES:ANNÉE 2025-2026,Séminaire Des mathématiques
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260423T110000
DTEND;TZID=Europe/Paris:20260423T120000
DTSTAMP:20260518T233349
CREATED:20260420T090126Z
LAST-MODIFIED:20260420T090126Z
UID:21319-1776942000-1776945600@www.math.ens.psl.eu
SUMMARY:Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distribution to Multivariate Settings
DESCRIPTION:Conformal prediction (CP) constructs uncertainty sets for model outputs with finite-sample coverage guarantees. A candidate output is included in the prediction set if its non-conformity score is not considered extreme relative to the scores observed on a set of calibration examples. However\, this procedure is only straightforward when scores are scalar-valued\, which has limited CP to real-valued scores or ad-hoc reductions to one dimension. The problem of ordering vectors has been studied via optimal transport (OT)\, which provides a principled method for defining vector-ranks and multivariate quantile regions\, though typically with only asymptotic coverage guarantees. We restore finite-sample\, distribution-free coverage by conformalizing the vector-valued OT quantile region. Here\, a candidate’s rank is defined via a transport map computed for the calibration scores augmented with that candidate’s score. This defines a continuum of OT problems for which we prove that the resulting optimal assignment is piecewise-constant across a fixed polyhedral partition of the score space. This allows us to characterize the entire prediction set tractably\, and provides the machinery to address a deeper limitation of prediction sets: that they only indicate which outcomes are plausible\, but not their relative likelihood. In one dimension\, conformal predictive distributions (CPDs) fill this gap by producing a predictive distribution with finite-sample calibration. Extending CPDs beyond one dimension remained an open problem. We construct\, to our knowledge\, the first multivariate CPDs with finite-sample calibration\, i.e.\, they define a valid multivariate distribution where any derived uncertainty region automatically has guaranteed coverage. We present both conservative and exact randomized versions\, the latter resulting in a multivariate generalization of the classical Dempster-Hill procedure.
URL:https://www.math.ens.psl.eu/evenement/beyond-uncertainty-sets-leveraging-optimal-transport-to-extend-conformal-predictive-distribution-to-multivariate-settings/
LOCATION:Salle W
CATEGORIES:CSD seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260427T140000
DTEND;TZID=Europe/Paris:20260427T150000
DTSTAMP:20260518T233349
CREATED:20260420T100943Z
LAST-MODIFIED:20260420T100944Z
UID:21334-1777298400-1777302000@www.math.ens.psl.eu
SUMMARY:Robin Khanfir - The Brownian tree is the only uniformly self-similar binary tree
DESCRIPTION:The Brownian tree is the scaling limit of many random tree models for which the square of the diameter is of the order of the number of vertices. In contrast to this universality\, proofs of such convergences commonly rely on model-specific methods. To provide a conceptual understanding of the universality of the Brownian tree\, we show that it is uniquely characterized by a uniform self-similar decomposition property. This leads to a general proof scheme for convergences to the Brownian tree that does not require the computation of finite-dimensional limit distributions. This talk is based on a work in progress.
URL:https://www.math.ens.psl.eu/evenement/robin-khanfir-the-brownian-tree-is-the-only-uniformly-self-similar-binary-tree/
LOCATION:Salle W (ENS)
CATEGORIES:Séminaire informel de probabilités
END:VEVENT
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