O-Minimality and Diophantine Geometry

This collection of articles, originating from a short course held at the University of Manchester, explores the ideas behind Pila''s proof of the Andre–Oort conjecture for products of modular curves. The basic strategy has three main ingredients: the Pila–Wilkie theorem, bounds on Galois orbits, and functional transcendence results. All of these topics are covered in this volume, making it ideal f...