On numbers, germs, and transseries

Matthias Aschenbrenner, Lou Van Den Dries, Joris Van Der Hoeven

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Germs of real-valued functions, surreal numbers, and transseries are three waysto enrich the real continuum by infinitesimal and infinite quantities. Each of thesecomes with naturally interacting notions of ordering and derivative. The category ofH-fields provides a common framework for the relevant algebraic structures. We givean exposition of our results on the model theory of H-fields, and we report on recentprogress in unifying germs, surreal numbers, and transseries from the point of view ofasymptotic differential algebra.

Original languageEnglish (US)
Title of host publicationInvited Lectures
EditorsBoyan Sirakov, Paulo Ney de Souza, Marcelo Viana
PublisherWorld Scientific Publishing Co. Pte Ltd
Pages19-42
Number of pages24
ISBN (Electronic)9789813272910
StatePublished - 2018
Event2018 International Congress of Mathematicians, ICM 2018 - Rio de Janeiro, Brazil
Duration: Aug 1 2018Aug 9 2018

Publication series

NameProceedings of the International Congress of Mathematicians, ICM 2018
Volume2

Conference

Conference2018 International Congress of Mathematicians, ICM 2018
CountryBrazil
CityRio de Janeiro
Period8/1/188/9/18

ASJC Scopus subject areas

  • Mathematics(all)

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