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H 1 The ordered differential field of transseries

Auteurs : van den Dries, Lou (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The field of Laurent series (with real coefficients, say) has a natural derivation but is too small to be closed under integration and other natural operations such as taking logarithms of positive elements. The field has a natural extension to a field of generalized series, the ordered differential field of transseries, where these defects are remedied in a radical way. I will sketch this field of transseries. Recently it was established (Aschenbrenner, Van der Hoeven, vdD) that the differential field of transseries also has very good model theoretic properties. I hope to discuss this in the later part of my talk.

    Codes MSC :
    03C60 - Model-theoretic algebra
    03C64 - Model theory of ordered structures; o-minimality
    12H05 - Differential algebra
    12L12 - Model theory

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 17/11/15
      Date de captation : 13/10/15
      Collection : Research talks ; Exposés de recherche ; Algebra ; Logic and Foundations
      Format : MP4
      Durée : 00:51:55
      Domaine : Algebra ; Logic and Foundations
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-10-13_Van_den_Dries.mp4

    Informations sur la rencontre

    Nom de la rencontre : Ordered algebraic structures and related topics / Structures algébriques ordonnées et leurs interactions
    Organisateurs de la rencontre : Broglia, Fabrizio ; Delon, Francoise ; Dickmann, Max ; Gondard, Danielle
    Dates : 12/10/15 - 16/10/15
    Année de la rencontre : 2015
    URL Congrès : http://conferences.cirm-math.fr/1155.html

    Citation Data

    DOI : 10.24350/CIRM.V.18863503
    Cite this video as: van den Dries, Lou (2015). The ordered differential field of transseries. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18863503
    URI : http://dx.doi.org/10.24350/CIRM.V.18863503


    Bibliographie

    1. Aschenbrenner, M., van den Dries, L., & van der Hoeven, J. (2015). Asymptotic differential algebra and model theory of transseries. - http://arxiv.org/abs/1509.02588

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