Retour Séminaire de Géométrie
Fields of generalized power series
Salma Kuhlmann
( U. Konstanz ) Salle 2
le 31 mai 2013 à 09:30
Fields of generalized power series are central objects in Model Theory and Algebra. They play an important role in:
- ordered algebraic structures (Hausdorff's lexicographic orders, Hahn's groups),
- non-standard models of arithmetic (integer parts),
- non-standard models of o-minimal expansions of the reals (exponentiation),
- model theory of valued fields (saturated and recursively saturated models, Ax-Kochen principles),
- real algebraic geometry (non-archimedean real closed fields),
- valuation theory (Kaplansky's embedding theorem),
- differential algebra (ordered differential fields, Hardy fields),
- difference algebra (automorphism groups),
- transcendental number theory (Schanuel's conjectures).
I will give an overview of my work with these fascinating objects in the last decade.