Seminar

Transseries originated some 25 years ago, mainly in Ecalle's work, but also independently in the study of Tarski's problem on the field of reals with exponentiation. Some 20 years ago I formulated some conjectures about the differential field of transseries, and started exploring its model-theoretic properties, first jointly with Matthias Aschenbrenner, and a few years later also in collaboration with Joris van der Hoeven. Around 2011 we finally saw a clear path towards a proof, sharpening the conjectures in the meantime. In the last few weeks we finished the job, with one proviso: as part of a division of labor and for lack of time, some final details have only been checked by some of us, but not yet by all three of us. In any case, I will motivate these conjectures, and give an account of their status.