The differential field of transseries extends the field of real Laurent series, and occurs in various context: asymptotic expansions, analytic vector fields, o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field, and report on our efforts to understand its first-order theory.

Authors: Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven

Keywords: Transseries, Hardy fields, differential fields, model completeness, NIP

A.M.S. subject classification: 03C64, 16W60, 26A12

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