Nigel Pynn-Coates: Asymptotic valued differential fields and differential-henselianity

Seminar will meet at 4:30pm Monday next week.

Mathematical logic seminar – Oct 1 2018 – NOTE UNUSUAL DAY AND TIME!
Time: 4:30pm – 5:30 pm

Room: Wean Hall 8220

Speaker: Nigel Pynn-Coates
Department of Mathematics
UIUC

Title: Asymptotic valued differential fields and differential-henselianity

Abstract:

It is well known that henselianity plays a fundamental role in the algebra and model theory of valued fields. The notion of differential-henselianity, introduced by Scanlon and developed in further generality by Aschenbrenner, van den Dries, and van der Hoeven, is a natural generalization to the setting of valued differential fields. I will present three related theorems justifying the position that differential-henselianity plays a similarly fundamental role in the algebra of asymptotic valued differential fields, a class arising naturally from the study of Hardy fields and transseries, and that have potential applications to the model theory of such fields.

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