Prof. Jonathan Pila FRS
Reader in Mathematical Logic
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Model theory and number theory.
Research page here with most of my papers in preprint form.
(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) 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. 53 (2020), 1-42.
(with N. Mok and J. Tsimerman) Ax-Schanuel for Shimura varieties, arXiv preprint here, Annals Math 189 (2019), 945-978.
(with J. Tsimerman) Independence of CM points in elliptic curves, JEMS (2021).
(with T. Scanlon) Effective transcendental Zilber-Pink, arXiv preprint, May 2021.
(with A. N. Shankar and J. Tsimerman, and with an appendix by H. Esnault and N. Groechenig) Canonical heights on Shimura varieties and the Andre-Oort conjecture, arXiv preprint, September 2021.
(with J. Tsimerman) Ax-Schanuel and exceptional integrability, arXiv preprint, February 2022.
Point-Counting and the Zilber-Pink Conjecture, CUP, 2022, see here.