### Abstract

The differential field of LE-series has very strong closure properties, and seems a perfect arena for asymptotic differential algebra. The theory of H-fields is an approach to develop a model theory for this differential field. I will discuss the field of LE-series, the subject of H-fields in general, and review the present state of an ongoing project on these matters in collaboration with Matthias Aschenbrenner and Joris van der Hoeven. The talk by Aschenbrenner will focus on recent progress.