Séminaires : Structures algébriques ordonnées

Equipe(s) : lm,
Responsables :F. Delon, M. Dickmann, D. Gondard, T. Servi
Email des responsables :
Salle : 1016
Adresse :Sophie Germain
Description


Mardi de 14h00 à 15h45
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Orateur(s) Mickaël Matusinski - Sur l'algébricité des séries de Puiseux,
Titre Surreal numbers as transseries... and vice versa !
Date06/02/2018
Horaire14:15 à 15:45
RésumeATTENTION : EXCEPTIONNELLEMENT, CET EXPOSÉ AURA LIEU À L'INSTITUT HENRI POINCARÉ.
Surreal numbers strike by the richness of their structure together with their universality: generalization of the reals and of the ordinal numbers, representation as generalized series with real coefficients, universal domain for real closed exponential fields. Several other important achievements have been obtained recently: structure of real differential field of transseries (Berarducci-Mantova), universal domain for Hardy fields (Aschenbrenner-van den Dries-van der Hoeven). Even a notion of partial composition has just been developed (Berarducci-Mantova).
In this talk, we'll get started with an intuitive presentation of surreal numbers (definitions and classical results). Then, we'll develop some aspects of the cited recent works. If time permits, we'll mention a work in progress with Berarducci, S. Kuhlmann and Mantova. We underline that this talk is also aimed to be complementary to the mini-course of A. Berarducci "Surreal models of the reals with exponentiation".
Salle1016
AdresseSophie Germain
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