The main focus of the program is to extend local resolution of singularities techniques in order to establish the o-minimality of certain expansions of the real field, such as those generated by the functions studied by Ilyashenko and Ecalle in his proof of Dulac’s problem. Over the last twenty years, the notion of o-minimal structure has become increasingly useful in the fields of real algebraic and real analytic geometry. Discovered by Van den Dries in the early 1980s and developed in its present model-theoretic generality soon after by Knight, Pillay and Steinhorn this notion provides a unifying framework for what is sometimes loosely referred to as tame real geometry. Since then, the development of o-minimality has been strongly influenced by real analytic geometry; this is apparent in the adaptation of methods of real analytic geometry to the o-minimal setting and in the motivation to find new and mathematically interesting examples of o-minimal structures. Conversely, model-theoretic methods available through the o-minimal point of view have led to new insights into real analytic geometry.

Many recent developments in the intersection of o-minimality and real analytic geometry use resolution of singularities in crucial ways, and they can in turn be viewed as extending the notion of resolution of singularities in the sense of the preparation theorems mentioned above. There is good reason to believe that extending resolution algorithms to certain classes of functions involving exponential scales may help shed new light on various interesting problems in real analytic geometry, coming from Pfaffian geometry and dynamical systems. Examples of particular interest to us are the classes of multisummable and of resurgent functions. The program's focus and main activities, two week-long workshops and three graduate courses, will be centered around the topics described above. There are of course many other developments both in o-minimality and in real anaytic geometry, and only the future will tell which of them may be relevant in addressing the questions discussed here. We intend to explore such developments in some of the mini-workshops.