This volume was produced in conjunction with the Thematic Program
in o-Minimal Structures and Real Analytic Geometry, held from
January to June of 2009 at the Fields Institute. Five of the six
contributions consist of notes from graduate courses associated
with the program: Felipe Cano on a new proof of resolution of
singularities for planar analytic vector fields; Chris Miller on
o-minimality and Hardy fields; Jean-Philippe Rolin on the
construction of o-minimal structures from quasianalytic classes;
Fernando Sanz on non-oscillatory trajectories of vector fields; and
Patrick Speissegger on pfaffian sets. The sixth contribution, by
Antongiulio Fornasiero and Tamara Servi, is an adaptation to the
nonstandard setting of A.J. Wilkie's construction of o-minimal
structures from infinitely differentiable functions. Most of this
material is either unavailable elsewhere or spread across many
different sources such as research papers, conference proceedings
and PhD theses. This book will be a useful tool for graduate
students or researchers from related fields who want to learn about
expansions of o-minimal structures by solutions, or images thereof,
of definable systems of differential equations.
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