Reader in Mathematical Logic
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
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, preprint here, Ann. Sci. Ecole Norm. Sup., to appear.
(with J. Tsimerman) Ax-Schanuel for the j-function, arXiv preprint here, Duke Math. J., to appear.
(with Capuano, Masser, and Zannier) Rational points on Grassmannians and unlikely intersections in tori, Bull. LMS 48 (2016), 141-154. Published version here.
(with J. Tsimerman) Multiplicative relations among singular moduli, arXiv preprint here.
On a modular Fermat equation, arXiv preprint here