Nigel Pynn-Coates, University of Illinois at Urbana-Champaign
"Asymptotic valued differential fields and differential-henselianity"
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 two 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. Time permitting, I will discuss potential applications to the model theory of such fields.
MC 5403