O-Minimality and Diophantine Geometry

A. J. Wilkie is the Fielden Professor of Pure Mathematics at the University of Manchester. He has twice been joint winner of the Association for Symbolic Logic's Karp Prize. He is a Fellow of the Royal Society, of the American Mathematical Society and a member of Academia Europaea. Wilkie recently served as President of the Association for Symbolic Logic from 2010 to 2013. G. O. Jones is a Researcher in the School of Mathematics at the University of Manchester.

Preface A. J. Wilkie and G. O. Jones; 1. The Manin–Mumford conjecture, an elliptic curve, its torsion points and their Galois orbits P. Habegger; 2. Rational points on definable sets A. J. Wilkie; 3. Functional transcendence via o-minimality Jonathan Pila; 4. Introduction to abelian varieties and the Ax–Lindemann–Weierstrass theorem Martin Orr; 5. The André–Oort conjecture via o-minimality Christopher Daw; 6. Lectures on elimination theory for semialgebraic and subanalytic sets A. J. Wilkie; 7. Relative Manin–Mumford for abelian varieties D. Masser; 8. Improving the bound in the Pila–Wilkie theorem for curves G. O. Jones; 9. Ax–Schanuel and o-minimality Jacob Tsimerman.