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X-WR-CALNAME:Département de mathématiques et applications
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
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TZOFFSETTO:+0200
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DTSTART:20240331T010000
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DTSTART:20241027T010000
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DTSTART;TZID=Europe/Paris:20240402T093000
DTEND;TZID=Europe/Paris:20240402T123000
DTSTAMP:20260406T051302
CREATED:20230830T101315Z
LAST-MODIFIED:20240325T080508Z
UID:16729-1712050200-1712061000@www.math.ens.psl.eu
SUMMARY:A critical drift-diffusion equation: intermittent behavior
DESCRIPTION:This talk is about a simple but rich model problem at the cross section of stochastic homogenization and singular stochastic PDE: We consider a drift-diffusion process with a time-independent and divergence-free random drift that is of white-noise character. As already realized in the physics literature\, the critical case of two space dimensions is most interesting: The elliptic generator requires a small-scale cut-off for well- posedness\, and one expects marginally super-diffusive behavior on large scales. I will explain the criticality of the two-dimensional case in the introductory course by scaling arguments. \nIn the presence of an (artificial) large-scale cut-off at scale L\, as a consequence of standard stochastic homogenization theory and its notion of a corrector\, there exist harmonic coordinates with a stationary gradient F ; the merit of these coordinates being that under their lens\, the drift-diffusion process turns into a martingale. I will revisit (qualitative) stochastic homogenization theory\nin the introductory course. \nIt has recently been established that the second moments diverge as 𝔼 |F|² ~ √ln L as L ↑ ∞. We show that in this limit\, |F|²/𝔼 |F|² is not equi-integrable\, while |det F |/𝔼 |F|² converges to zero (in probability). This suggests that any limit\, if it exists\, will not admit a simple characterization. \nWe establish this asymptotic behavior by characterizing a proxy F̃  introduced in previous work as the solution of an Itô SDE w. r. t. the variable L\, and which implements the concept of a scale-by-scale homogenization. For this proxy\, we establish 𝔼|F̃ |⁴ ≫ (𝔼|F̃ |²)² and 𝔼(det F̃ )² ≲ 1. In view of the former property\, we assimilate this phenomenon to intermittency. I will try to elucidate the idea of scale-by-scale homogenization in the introductory course. \nThis is joint work with G. Chatzigeorgiou\, P. Morfe\, L. Wang\, and with C. Wagner.
URL:https://www.math.ens.psl.eu/evenement/felix-otto/
LOCATION:ENS – salle W\, 45 rue d'Ulm\, Paris\, 75005\, France
CATEGORIES:Séminaire Analyse non linéaire et EDP
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20240403T110000
DTEND;TZID=Europe/Paris:20240403T120000
DTSTAMP:20260406T051302
CREATED:20240119T110825Z
LAST-MODIFIED:20240119T110825Z
UID:17186-1712142000-1712145600@www.math.ens.psl.eu
SUMMARY:Catherine Goldstein\, raconte-moi Charles Hermite !
DESCRIPTION:
URL:https://www.math.ens.psl.eu/evenement/catherine-goldstein-raconte-moi-charles-hermite/
LOCATION:DMA Salle W
CATEGORIES:Algèbre et géométrie,Séminaire Raconte-moi
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20240403T131500
DTEND;TZID=Europe/Paris:20240403T141500
DTSTAMP:20260406T051302
CREATED:20240329T082614Z
LAST-MODIFIED:20240329T082701Z
UID:17345-1712150100-1712153700@www.math.ens.psl.eu
SUMMARY:Le modèle de dimères en mécanique statistique
DESCRIPTION:Le modèle de dimères représente la répartition de molécules di-atomiques sur la surface d’un cristal. Il appartient à la grande famille des modèles de mécanique statistique définis sur les graphes\, dont d’autres représentant célèbres sont le modèle d’Ising et la percolation.  \n  \nAprès une introduction générale\, nous nous intéresserons aux résultats fondateurs du modèle de dimères lorsque le graphe sous-jacent est fini\, en particulier au théorème de Kasteleyn qui prouve une formule close pour le nombre de configurations de dimères.
URL:https://www.math.ens.psl.eu/evenement/modele-dimeres-mecanique-statistique/
LOCATION:amphi Galois NIR
CATEGORIES:ANNÉE 2023-2024
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20240404T120000
DTEND;TZID=Europe/Paris:20240404T140000
DTSTAMP:20260406T051302
CREATED:20240502T082427Z
LAST-MODIFIED:20240502T082427Z
UID:17436-1712232000-1712239200@www.math.ens.psl.eu
SUMMARY:ENS-Data Science colloquium - Lénaïc Chizat (EPFL)
DESCRIPTION:04 Avril 2024\, Lénaïc Chizat (EPFL)\nTitle: A Formula for Feature Learning in Large Neural Networks\nAbstract: Deep learning succeeds by doing hierarchical feature learning\, but tuning hyperparameters such as initialization scales\, learning rates\, etc.\, only give indirect control over this behavior. This calls for theoretical tools to predict\, measure and control feature learning. In this talk\, we will first review various theoretical advances (signal propagation\, infinite width dynamics\, etc) that have led to a better understanding of the subtle impact of hyperparameters and architectural choices on the training dynamics. We will then introduce a formula which\, in any architecture\, quantifies feature learning in terms of more tractable quantities: statistics of the forward and backward passes\, and a notion of alignment between the feature updates and the backward pass which captures an important aspect of the nature of feature learning. This formula suggests normalization rules for the forward and backward passes and for the layer-wise learning rates. To illustrate these ideas\, I will discuss the feature learning behavior of ReLU MLPs and ResNets in the infinite width and depth limit.
URL:https://www.math.ens.psl.eu/evenement/ens-data-science-colloquium-lenaic-chizat-epfl/
LOCATION:Amphi Jaurès (29 Rue d’Ulm)
CATEGORIES:Séminaire Data de l’ENS
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20240416T140000
DTEND;TZID=Europe/Paris:20240416T170000
DTSTAMP:20260406T051302
CREATED:20240404T093514Z
LAST-MODIFIED:20240404T094628Z
UID:17358-1713276000-1713286800@www.math.ens.psl.eu
SUMMARY:Group theory seminar Jaikin-Zapirain/Marquis/Kharlampovich
DESCRIPTION:April 16 (Tuesday) \nFor this seminar we will have the pleasure of listening to three talks:\n\n14.00 – 14.45 Andrei Jaikin-Zapirain (UAM)\, « Compressed subgroups in free groups are inert »\n\n15.00 – 15.45 Timothée Marquis (UCL)\, « Amalgams of rational unipotent groups and residual nilpotence ».\n\n16.15 – 17.00 Olga Kharlampovich (CUNY)\, « Quantification of separability of cubically convex-cocompact subgroups of RAAGs via representations ».\n\n\n\n Andrei Jaikin-Zapirain  « Compressed subgroups in free groups are inert ».  \n Let F be a free group. A finitely generated subgroup H is called compressed in F if it is not contained in a subgroup of F of smaller rank than H\, and it is called inert in F if H ∩ U is compressed in U for any subgroup U of F. In my talk\, I will show that compressed subgroups are also inert. The solves a conjecture of Dicks and Ventura from 1996. \nTimothée Marquis \, « Amalgams of rational unipotent groups and residual nilpotence ». \n Given a group property (P)\, a group G is called residually (P) if every nontrivial element of G has a nontrivial image in some quotient of G that satisfies (P). The study of residual properties of graphs of groups has a long and rich history\, originating from Magnus’ theorem that free groups are residually torsionfree nilpotent. In this talk\, I will start by reviewing a few key results of this history\, before presenting an intriguing phenomenon concerning the residual nilpotence of certain amalgams of rational unipotent groups. Joint work with Pierre-Emmanuel Caprace.  \nOlga Kharlampovich\,   « Quantification of separability of cubically convex-cocompact subgroups of RAAGs via representations« . \n We answer the question asked by Louder\, McReinolds and Patel and prove the following statement. Let L be a RAAG\, H a cubically convex-cocompact subgroup of L\, then there is a finite dimensional representation of L that separates the subgroup H in the induced Zariski topology. As a corollary\, we establish a polynomial upper bound on the size of the quotients used to separate H in L. This implies the same statement for a virtually special group L and\, in particular\, a fundamental group of a hyperbolic 3-manifold. For any finitely generated subgroup H of a limit group L we prove the same results and\, in addition\, show that there exists a finite-index subgroup K containing H\, such that K is a subgroup of a group obtained from H by a series of extensions of centralizers and free products with infinite cyclic group. If H is non-abelian\, the K is fully residually H. A corollary is that a hyperbolic limit group satisfies the Geometric Hanna Neumann conjecture. These are joint results with K. Brown and A. Vdovina. \n\nOrganized by Andrei Alpeev\, Laurent Bartholdi\, Anna Erschler and Panagiotis Tselekidis  \nPartially supported by ERC Advanced Grant 101097307 (P.I.:Laurent Bartholdi).
URL:https://www.math.ens.psl.eu/evenement/group-theory-seminar-jaikin-zapirain-marquis-kharlampovich/
LOCATION:14:00-17:00 Salle W
CATEGORIES:Séminaire de théorie des groupes à l’ENS
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20240422T110000
DTEND;TZID=Europe/Paris:20240422T120000
DTSTAMP:20260406T051302
CREATED:20231120T122350Z
LAST-MODIFIED:20240415T094914Z
UID:17005-1713783600-1713787200@www.math.ens.psl.eu
SUMMARY:Piet Lammers: The 2D XY model and its relation to height functions.
DESCRIPTION:
URL:https://www.math.ens.psl.eu/evenement/piet-lammers-titre-a-preciser/
LOCATION:DMA Salle W
CATEGORIES:Probabilités et statistiques,Séminaire informel de probabilités
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20240430T093000
DTEND;TZID=Europe/Paris:20240430T123000
DTSTAMP:20260406T051302
CREATED:20230830T101424Z
LAST-MODIFIED:20240426T060337Z
UID:16733-1714469400-1714480200@www.math.ens.psl.eu
SUMMARY:CANCELED - Camillo De Lellis - CANCELED
DESCRIPTION:Mini-course: Flows of nonsmooth vector fields \nConsider a vector field v on the Euclidean space. The classical Cauchy-Lipschitz (also named Picard-Lindelöf) Theorem states that\, if the vector field is Lipschitz in space\, for every initial datum x there is a unique trajectory γ starting at x at time 0 and solving the ODE γ'(t) = v(t\, γ(t)). The theorem looses its validity as soon as v is slightly less regular. However\, if we bundle all trajectories into a global map allowing x to vary\, a celebrated theory started by DiPerna and Lions in the 80es shows that there is a unique such flow under very reasonable conditions and for much less regular vector fields. This has a lot of repercussions to several important partial differential equations where the idea of « following the trajectories of particles » plays a fundamental role. In this lecture I will review the fundamental ideas of the original theory\, an alternative approach due to Gianluca Crippa and myself\, and review a series of natural questions. Some of these questions will be answered in the second part. \nLecture: Transport equations and anomalous dissipation \nAfter mentioning the fundamental theorems of DiPerna-Lions and Ambrosio on flows of Sobolev vector fields we will explore a number of sharpness questions related to them (a more detailed and elementary overiew of the theorems and of the sharpness questions will already have been given in the previous lecture\, but anyway this seminar will be arranged so that it can be followed independently from the latter). Many of these questions have been at least partially answered in the last few years and I will first survey what is the overall understanding which we have gained on them. I will then focus on a particular one and highlight its link with a phenomenon which is poorly understood at the rigorous mathematical level: the occurrence of the so-called anomalous dissipation in incompressible fluid dynamics.
URL:https://www.math.ens.psl.eu/evenement/camillo-de-lellis/
LOCATION:Jussieu —  salle 15-16-309\, 4 Place Jussieu\, Paris\, 75005\, France
CATEGORIES:Séminaire Analyse non linéaire et EDP
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