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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
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TZNAME:CEST
DTSTART:20210328T010000
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DTSTART:20211031T010000
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20211011T140000
DTEND;TZID=Europe/Paris:20211011T170000
DTSTAMP:20260526T014752
CREATED:20211011T120000Z
LAST-MODIFIED:20211104T133512Z
UID:14131-1633960800-1633971600@www.math.ens.psl.eu
SUMMARY:Après-midi de théorie de groupes
DESCRIPTION:14.00 – 14.45 François Le Maître (Université Paris Diderot -Paris VII)\, Reconstruction for Boolean measure-preserving actions of full groups and applications15.00 – 15.45 Romain Tessera (Université Paris Diderot -Paris VII)\, Coarse geometry meets measured group theory16.00 – 16.45 Pierre Fima (Université Paris Diderot -Paris VII)\, Highly transitive groups among groups acting on trees
URL:https://www.math.ens.psl.eu/evenement/apres-midi-de-theorie-de-groupes-17/
LOCATION:Salle W (DMA ENS)
CATEGORIES:Séminaire de théorie des groupes à l’ENS
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20211012T093000
DTEND;TZID=Europe/Paris:20211012T123000
DTSTAMP:20260526T014752
CREATED:20211012T073000Z
LAST-MODIFIED:20211108T210837Z
UID:8581-1634031000-1634041800@www.math.ens.psl.eu
SUMMARY:The Rayleigh-Bénard convection problem
DESCRIPTION:Rayleigh-Bénard convection is the buoyancy-driven flow of a fluid heated from below and cooled from above and is a paradigm for nonlinear dynamics with important applications to meteorology\, oceanography and engineering. We are interested in obtaining quantitative bounds on the Nusselt number\, the vertical heat transport enhancement factor. The Nusselt number\, besides being an interesting quantity for engineering applications\, it is the natural quantity to measure the intensity and effectiveness of the motion. For this reason\, we are interested in proving (upper) bounds which catch the relation between the Nusselt number and the (nondimensional control parameter) Rayleigh number\, in turbulent regimes. Despite great scientific developments in this field in the last 30 years\, it is still not clear what role the boundary conditions play in the scaling laws for the Nusselt number. In this talk we address this problem\, establishing rigorous bounds for the Rayleigh-Bénard convection problem with Navier-slip boundary conditions for the velocity. We employ the background field method and deal with a careful PDE analysis\, given the production of vorticity at the walls. In conclusion\, we relate this result to other bounds derived for no-slip and stress-free boundary conditions and discuss open problems. This seminar is based on a joint work with T. Drivas and H. Nguyen.
URL:https://www.math.ens.psl.eu/evenement/the-effect-of-boundary-conditions-for-the-velocity-on-scaling-laws-in-the-rayleigh-benard-convection-problem/
LOCATION:Jussieu (salle 15-16-309)
CATEGORIES:Séminaire Analyse non linéaire et EDP
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20211013T130000
DTEND;TZID=Europe/Paris:20211013T143000
DTSTAMP:20260526T014752
CREATED:20220217T102623Z
LAST-MODIFIED:20220217T102623Z
UID:15244-1634130000-1634135400@www.math.ens.psl.eu
SUMMARY:n! (30n)! / (6n)! (10n)! (15n)!
DESCRIPTION:Ces quotients de factorielles sont toujours des nombres entiers\, essayez de le prouver en calculant leur valuation p-adique ! Derrière cette propriété élémentaire se cache le fait qu’une certaine fonction hypergéométrique est algébrique\, comme l’a observé Rodríguez Villegas il y a quinze ans. Je prendrai son théorème — que j’aurais tant voulu démontrer moi-même — comme excuse pour parler de l’une des plus belles idées des maths\, la monodromie\, et de comment reconnaître les fonctions algébriques parmi les solutions d’équations différentielles linéaires.
URL:https://www.math.ens.psl.eu/evenement/n-30n-6n-10n-15n/
LOCATION:ENS (amphithéâtre Galois sous la bibliothèque de mathématique)
CATEGORIES:ANNÉE 2021-2022,Séminaire Des mathématiques
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20211021T104500
DTEND;TZID=Europe/Paris:20211021T114500
DTSTAMP:20260526T014752
CREATED:20211109T150605Z
LAST-MODIFIED:20211109T150733Z
UID:14472-1634813100-1634816700@www.math.ens.psl.eu
SUMMARY:Machine learning and applied mathematics
DESCRIPTION:The recent success of machine learning suggests that neural networks may be capable of approximating high-dimensional functions with controllably small errors. As a result\, they could outperform standard function interpolation methods that have been the workhorses of scientific computing but do not scale well with dimension. In support of this prospect\, here I will review what is known about the trainability and accuracy of shallow neural networks\, which offer the simplest instance of nonlinear learning in functional spaces that are fundamentally different from classic approximation spaces. The dynamics of training in these spaces can be analyzed using tools from optimal transport and statistical mechanics\, which reveal when and how shallow neural networks can overcome the curse of dimensionality. I will also discuss how scientific computing problem in high-dimension once thought intractable can be revisited through the lens of these results\, focusing on applications related to (i) solving Fokker-Planck equations associated with high-dimensional systems displaying metastability and (ii) sampling Boltzmann-Gibbs distributions using generative models to assist MCMC methods.
URL:https://www.math.ens.psl.eu/evenement/machine-learning-and-applied-mathematics/
LOCATION:Amphi Jaurès (29 Rue d’Ulm)
CATEGORIES:Séminaire Data de l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20211027T130000
DTEND;TZID=Europe/Paris:20211027T143000
DTSTAMP:20260526T014752
CREATED:20220217T102530Z
LAST-MODIFIED:20220217T102530Z
UID:15241-1635339600-1635345000@www.math.ens.psl.eu
SUMMARY:Surfaces hyperboliques et leurs systoles
DESCRIPTION:Dans cet exposé\, je vais expliquer comment on peut construire des surfaces hyperboliques à partir de morceaux de ce qu’on appelle le plan hyperbolique. Je parlerai de courbes sur ces surfaces et d’un problème ouvert à propos des courbes « très courtes ».
URL:https://www.math.ens.psl.eu/evenement/surfaces-hyperboliques-et-leurs-systoles/
LOCATION:ENS (amphithéâtre Galois sous la bibliothèque de mathématique)
CATEGORIES:ANNÉE 2021-2022,Séminaire Des mathématiques
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