Asymptotic differential algebra aims at studying the asymptotic behavior of solutions to differential equations using techniques from differential algebra and valuation theory. One central concept is that of an H-field: a differential field with an ordering that satisfies natural compatibility conditions with respect to the derivation. Natural examples of H-fields are Hardy fields and the field of transseries. It turns out that both the field of transseries and maximal Hardy fields are “H-closed” and their first theory order is now well understood. In our talk, we will survey these and some other results, which are the fruits of a long collaboration with Matthias Aschenbrenner and Lou van den Dries.

Occasion: NCMIS distinguished lecture, Beijing, China, September 15, 2026

Documents: slideshow, TeXmacs source