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H 1 Smooth parametrizations in analysis, dynamics, and diophantine geometry

Auteurs : Yomdin, Yosef (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Smooth parametrization consists in a subdivision of mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the talk is to provide a short overview of some results and open problems on smooth parametrization and its applications in several apparently separated domains: Smooth Dynamics, Diophantine Geometry, and Approximation Theory. The structure of the results, open problems, and conjectures in each of these domains shows in many cases a remarkable similarity, which I’ll try to stress. Sometimes this similarity can be easily explained, sometimes the reasons remain somewhat obscure, and it motivates some natural questions discussed in the talk. I plan to present also some new results, connecting smooth parametrization with “Remez-type” (or “Norming”) inequalities for polynomials restricted to analytic varieties.

    Codes MSC :
    11Gxx - Arithmetic algebraic geometry (Diophantine geometry) [See also 11Dxx, 14Gxx, 14Kxx]
    37C05 - Smooth mappings and diffeomorphisms
    41A46 - Approximation by arbitrary nonlinear expressions; widths and entropy

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 25/06/15
      Date de captation : 11/06/15
      Collection : Research talks ; Dynamical Systems and Ordinary Differential Equations ; Algebraic and Complex Geometry ; Number Theory
      Format : quicktime ; audio/x-aac
      Durée : 00:47:56
      Domaine : Dynamical Systems & ODE ; Number Theory ; Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-06-11_Yomdin.mp4

    Informations sur la rencontre

    Nom de la rencontre : Real analytic geometry and trajectories of vector fields / Géométrie analytique réelle et trajectoires de champs de vecteurs
    Organisateurs de la rencontre : Kurdyka, Krzysztof ; Parusinski, Adam ; Rolin, Jean-Philippe ; Sanz, Fernando
    Dates : 08/06/15 - 12/06/15
    Année de la rencontre : 2015
    URL Congrès : http://conferences.cirm-math.fr/1220.html

    Citation Data

    DOI : 10.24350/CIRM.V.18772203
    Cite this video as: Yomdin, Yosef (2015). Smooth parametrizations in analysis, dynamics, and diophantine geometry. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18772203
    URI : http://dx.doi.org/10.24350/CIRM.V.18772203


    Bibliographie

    1. Yomdin, Y. (2014). Smooth parametrizations in dynamics, analysis, diophantine and computational geometry. - http://arxiv.org/abs/1406.1719

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