**October 22**

Matthias Aschenbrenner,
University of Vienna

**The elementary theory of maximal Hardy fields**

A Hardy field is a differential field of germs at infinity of one-variable differentiable real-valued functions defined on half-lines. Hardy fields appear naturally in model theory and its applications to real analytic geometry and dynamical systems, and also have found uses in computer algebra, ergodic theory, and various other fields of mathematics. I will discuss some optimal extension results for Hardy fields obtained in the last few years, which lead to a description of the theory of maximal Hardy fields and applications to ordinary differential equations. (This is joint work with Lou van den Dries and Joris van der Hoeven.)