**February 21**

**Patrick Speissegger**,
McMaster University

**A new Hardy field of relevance to Hilbert's 16th problem**

In our paper, we construct a Hardy field that embeds, via a map representing asymptotic expansion, into the field of transseries as described by Aschenbrenner, van den Dries and van der Hoeven in the recent seminal book. This Hardy field extends that of the o-minimal structure generated by all restricted analytic functions and the exponential function, and it contains Ilyashenko's almost regular germs. I will describe how this Hardy field arises quite naturally in the study of Hilbert's 16th problem and give an outline of its construction. (Joint work with Zeinab Galal and Tobias Kaiser.)