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Documents  Aschenbrenner, Matthias | enregistrements trouvés : 4

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Research talks;Algebraic and Complex Geometry;Logic and Foundations

The concept of a "transseries" is a natural extension of that of a Laurent series, allowing for exponential and logarithmic terms. Transseries were introduced in the 1980s by the analyst Écalle and also, independently, by the logicians Dahn and Göring. The germs of many naturally occurring real-valued functions of one variable have asymptotic expansions which are transseries. Since the late 1990s, van den Dries, van der Hoeven, and myself, have pursued a program to understand the algebraic and model-theoretic aspects of this intricate but fascinating mathematical object. A differential analogue of “henselianity" is central to this program. Last year we were able to make a significant step forward, and established a quantifier elimination theorem for the differential field of transseries in a natural language. My goal for this talk is to introduce transseries without prior knowledge of the subject, and to explain our recent work. The concept of a "transseries" is a natural extension of that of a Laurent series, allowing for exponential and logarithmic terms. Transseries were introduced in the 1980s by the analyst Écalle and also, independently, by the logicians Dahn and Göring. The germs of many naturally occurring real-valued functions of one variable have asymptotic expansions which are transseries. Since the late 1990s, van den Dries, van der Hoeven, and myself, have ...

03C10 ; 03C64 ; 26A12

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- xxi; 849 p.
ISBN 978-0-691-17543-0

Annals of mathematics studies

Localisation : Ouvrage RdC (ASCH)

série arithmétique # série divergente # expansion asymptotique # algèbre différentielle

12-02 ; 03-02 ; 12L12 ; 12H05 ; 03C64

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- xiv; 215 p.
ISBN 978-3-03719-154-5

EMS series of lectures in mathematics

Localisation : Ouvrage RdC (ASCH)

variété topologique à 3 dimensions # groupe fondamental # théorème de géométrisation # 3-variété hyperbolique # groupe spécial

57M05 ; 57M27 ; 20E26 ; 57-02 ; 57M50 ; 57N10 ; 20F65

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- vii; 100 p.
ISBN 978-0-8218-8801-8

Memoirs of the american mathematical society , 1058

Localisation : Collection 1er étage

théorie des groupes # variétés de dimension 3 # groupe fondamental

20E26 ; 57M05 ; 20E06 ; 20E22

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