Reader in Mathematical Logic
+44 1865 273527
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, 2011-2016
Editor, Algebra and Number Theory
Editor, International Journal of Number Theory
Editor, Forum of Mathematics
Editor, IMRN
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 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. 49 (2016), 813-858.
(with J. Tsimerman) Ax-Schanuel for the j-function, arXiv preprint here, Duke Math. J. 165 (2016), 2587-2605.
(with R. Cluckers and A. J. Wilkie) Uniform parameterization of subanalytic sets and diophantine applications, arXiv preprint here, Ann. Sci. Ecole Norm. Sup., to appear.
(with N. Mok and J. Tsimerman) Ax-Schanuel for Shimura varieties, arXiv preprint here.