Séminaires : Structures algébriques ordonnées

Equipe(s) : lm,
Responsables :F. Delon, M. Dickmann, D. Gondard
Email des responsables : dickmann@math.univ-paris-diderot.fr
Salle : 1016
Adresse :Sophie Germain

Mardi de 14h00 à 15h45
Page du séminaire et programme
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Orateur(s) Vincent Bagayoko - Univ. Mons (Belgique),
Titre Hyperseries and surreal numbers
Horaire14:00 à 15:45
Diffusion Code: 479120
RésumeTransseries are formal series, involving exponentials and logarithms, which provide a natural model for the model theory of Hardy fields, i.e. ordered fields of real-valued differentiable germs. Transseries are not closed under many functional equations, whose solutions still behave like germs in Hardy fields. Hyperexponential functions, which grow faster or than any finite iteration of the exponential, naturally appear in this context. Although such functions are somewhat analytically exotic, the works of Ecalle, van der Hoeven and Schmeling show that some of them are amenable to geometric or formal descriptions. Hyperseries are an extension of transseries that can act as formal counterparts to more general germs including hyperexponentials. It turns out that hyperseries can be interpreted as Conway's surreal numbers. I will show that surreal numbers fill the gaps left in transseries, and I will explain how one can exploit this connection to endow the class of surreal numbers with a structure of field of hyperseries.
AdresseZoom Id 835 5210 4627