Reader in Mathematical Logic
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Research Interests:
Model theory and number theory.
Research page here with most of my papers in preprint form.
Further Details:
Editor, Proceedings of the Edinburgh Mathematical Society
Editor, Algebra and Number Theory
Editor, International Journal of Number Theory
Editor, Forum of Mathematics
Prizes, Awards, and Scholarships:
Major / Recent Publications:
(with E. Bombieri) The number of integral points on arcs and ovals, Duke Math. J. 59 (1989) 337–357. Copyright 1989, Duke University Press. Preprint version reprinted here by permission of the publisher.
(with A. J. Wilkie) The rational points of a definable set, Duke Math. J. 133 (2006) 591-616, published by Duke University Press. Preprint version reprinted here by permission of the publisher.
(with U. Zannier) Rational points in periodic analytic sets and the Manin-Mumford conjecture, Rend. Mat. Acc. Lincei 19 (2008) 149–162. Preprint version reprinted here by permission of the publisher.
O-minimality and the Andre-Oort conjecture for C^n, Annals Math. 173 (2011), 1779-1840. Preprint version here.
(with P. Habegger) Some unlikely intersections beyond Andre-Oort, Compositio 148 (2012), 1-27. Preprint version here.
(with J. Tsimerman) The Andre-Oort conjecture for the moduli space of Abelian surfaces, Compositio 149 (2013), 204-216, arXiv version here.
(with J. Tsimerman) Ax-Lindemann for A_g, Annals Math. 179 (2014), 659-681, and arXiv preprint here.
(with P. Habegger) O-minimality and certain atypical intersections, submitted, preprint here.
(with J. Tsimerman) Ax-Schanuel for the j-function, arXiv preprint here.
(with J. Tsimerman) Multiplicative relations among singular moduli, arXiv preprint here.