TY - GEN
T1 - On numbers, germs, and transseries
AU - Aschenbrenner, Matthias
AU - Van Den Dries, Lou
AU - Van Der Hoeven, Joris
N1 - Funding Information:
The first-named author was partially support by NSF Grant DMS-1700439. MSC2010: primary 03C64; secondary 12J15, 12J20, 34M15.
Publisher Copyright:
© Proceedings of the International Congress of Mathematicians, ICM 2018. All rights reserved.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
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M3 - Conference contribution
AN - SCOPUS:85075185669
T3 - Proceedings of the International Congress of Mathematicians, ICM 2018
SP - 19
EP - 42
BT - Invited Lectures
A2 - Sirakov, Boyan
A2 - de Souza, Paulo Ney
A2 - Viana, Marcelo
PB - World Scientific Publishing Co. Pte Ltd
T2 - 2018 International Congress of Mathematicians, ICM 2018
Y2 - 1 August 2018 through 9 August 2018
ER -