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DTSTART;TZID=Europe/Paris:20261110T093000
DTEND;TZID=Europe/Paris:20261110T123000
DTSTAMP:20261110T001142
CREATED:20260717T114620Z
LAST-MODIFIED:20261108T124254Z
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SUMMARY:Monica Musso –  The Liquid Drop Model: From Minimizers to Non-Spherical Equilibria
DESCRIPTION:Speaker: Monica Musso\, University of Bath \n\n\n\nAbstract for the mini course: Introduction to the Liquid Drop Model: Minimizers\, Stability and Nonexistence \n\n\n\nThe liquid drop model\, introduced by Gamow to describe atomic nuclei\, is a classical problem in the calculus of variations involving the competition between surface tension\, which favours compact shapes\, and Coulomb repulsion\, which favours spreading and fragmentation. \n\n\n\nIn this introductory lecture\, I will present the mathematical formulation of the model and review some fundamental results concerning the existence and geometry of energy minimizers. Particular attention will be given to the role of balls\, their minimality and stability properties\, and the nonexistence of minimizers for sufficiently large masses. I will discuss the main mathematical ideas behind these results\, as well as some open questions. \n\n\n\nAbstract for the talk: Beyond Minimizers: Constructing Non-Spherical Equilibria \n\n\n\nWhile balls are stationary configurations for the liquid drop energy at every volume\, the existence of other critical points is a much more delicate question. \n\n\n\nIn this talk\, I will discuss recent results on the existence and construction of smooth\, compact\, non-spherical equilibria of the liquid drop model\, in both the small- and large-mass regimes. For small masses\, I will describe the construction of configurations consisting of two nearly spherical regions connected by a very thin catenoidal neck. For large masses\, I will present equilibria resembling necklaces of pearls\, whose geometry is related to Delaunay unduloids. I will also discuss bifurcation phenomena from spherical equilibria\, which give rise to further families of non-spherical stationary configurations. \n\n\n\nThe emphasis will be on the geometric ideas and analytical techniques behind these results\, particularly singular perturbation methods and Lyapunov–Schmidt reduction. Together\, these constructions reveal the richness of the critical point structure of the liquid drop energy\, far beyond the theory of minimizers. \n\n\n\nThis work is in collaboration with M. del Pino\, F. De Regibus\, R. Frank\, M. Grossi and A. Zuñiga.
URL:https://www.math.ens.psl.eu/evenement/monica-musso-university-of-bath/
LOCATION:Amphithéâtre Choquet-Bruhat – IHP\, 11 Rue Pierre et Marie Curie\, Paris\, 75005
CATEGORIES:Séminaire Analyse non linéaire et EDP
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DTSTART;TZID=Europe/Paris:20261110T120000
DTEND;TZID=Europe/Paris:20261110T130000
DTSTAMP:20261110T001142
CREATED:20261109T091349Z
LAST-MODIFIED:20261109T091351Z
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SUMMARY:ENS-Data Science colloquium - Pierre Gentine (Columbia University) : Lost in latent land
DESCRIPTION:Machine learning and artificial intelligence have been revolutionizing weather and climate modeling and data analysis over the past few years. However\, it remains unclear how much understanding has been gained from those models\, even though they are reaching unprecedented accuracy. Through the study and analysis of carefully chosen latent spaces\, I will demonstrate how we can get new understanding on the terrestrial water and carbon cycle as well as on atmospheric processes\, specifically on convection. Those latent spaces can also be used to better characterize complex stochastic processes such as turbulence and combined with data assimilation in order to achieve improved performance in those models \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-pierre-gentine-columbia-university-lost-in-latent-land/
LOCATION:Amphi Jean Jaurès\, 29 rue d'Ulm\, PARIS\, 75005\, France
CATEGORIES:ENS-Data Science colloquium
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