The course is based on joint work with Matthias Aschenbrenner and Joris van der Hoeven. The focus of our book ``Asymptotic Differential Algebra and Model Theory of Transseries’'  (Annals of Mathematics Studies 195, 2017, Princeton University Press) was on understanding the differential field of transseries. In the process we developed a wide ranging theory of rather general valued differential fields.

The purpose of the course is to apply this material to the study of Hardy fields, which are intriguing mathematical structures with a history going back to Du Bois-Reymond, Veronese,  Borel, Hardy, Hausdorff, and Hahn, to mention some pioneers of over a century ago. Many formerly open problems about Hardy fields can now be answered, and interesting new problems can be posed. I will discuss also potential connections to o-minimality.

Hardy fields are algebraic as well as analytic in nature, so we are going to use also some analysis (real, complex, functional, ODE), plus a modest amount of model theory. I will try to make this course as self-contained as possible, but sometimes it will be inevitable to refer to the literature, like the book already mentioned, for proofs of auxiliary results. My two Fields workshop talks (January 11, 13)  are meant as an introduction to the course: http://www.fields.utoronto.ca/activities/21-22/tame-intro . 

Prof. Lou van den Dries will have question sessions on the following dates (from 11 to 12 EST): February 10, February 24, March 10, March 24. There will also be an additional Q&A session on April 7 at 11:10 AM.