This is my personal website. For my staff page, click here.

Events

• I am  the University of Reading node for the GWNT seminar, which receives financial support from the LMS and others. The next seminar will take place at the University of Bath on Thursday 18th September.

Postdocs and PhDs

• I am very happy to support postdoctoral fellowship applications hosted at the University of Reading, such as those through Marie-Curie, EPSRC, Royal Commission for the Exhibition of 1851, LMS, Leverhulme, etc. 

• I am also very happy to support PhD applicants to the University who are interested in number theory, arithmetic geometry, or any of the other topics relevant to my work.

Publications and preprints

• Unlikely intersections in Shimura varieties and beyond: a survey, arXiv:2506.02900

• The large Galois orbits conjecture under multiplicative degeneration, with M. Orr, arXiv:2306.13463 

• A note on unlikely intersections in Shimura varieties, with V. Aslanyan, Journal of Number Theory, Volume 260, 2024, 212-222 (open access), errata

• Zilber-Pink in a product of modular curves assuming multiplicative degeneration, with M. Orr, to appear in Duke Math., arXiv:2208.06338

• The model theory of canonical models of modular curves, with B. Zilber, to appear in Current Developments in Hodge Theory — Proceedings of Hodge Theory at IMSA,  edited by P. Griffiths, L. Katzarkov, C. Simpson, Simons Symposia, Springer (based on unpublished works arXiv:2107.11110, arXiv:2106.06387)

• Effective computations for weakly optimal subvarieties, with G. Binyamini, arXiv:2105.12760, to appear in J. Eur. Math. Soc.

• Lattices with skew-Hermitian forms over division algebras and unlikely intersections, with M. Orr, J. Éc. polytech., Math., Tome 10 (2023), p. 1097-1156 (open access)

• The space of homogeneous probability measures on [the maximal Satake compactification] is compact, with A. Gorodnik and E. Ullmo, with an appendix by Jialun Li, Math. Ann. 386, 987-1016 (2023) (open access)

• Zilber-Pink in [a product of modular curves], Diophantische Approximationen. Oberwolfach Rep. 19 (2022), no. 2, pp. 1091–1164, (open access version)

• Quantitative reduction theory and unlikely intersections, with M. Orr, IMRN 2022(20), 16138-16195 (open access)

• Unlikely intersections with E x CM curves in [the moduli space of principally polarized abelian surfaces], with M. Orr, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XXII (2021), 1705-1745, arXiv:1902.10483

• Convergence of measures on compactifications of locally symmetric spaces, with A. Gorodnik and E. Ullmo, Mathematische Zeitschrift, 297(3), 1293-1328 (2021) (open access)

• Effective estimates for the degrees of maximal special subvarieties, with A. Javanpeykar and L. Kühne, Sel. Math. New Ser. 26, 2 (2020) (open access)

• Conjugation of semisimple subgroups over real number fields of bounded degree, with M. Borovoi and J. Ren, Proc. Amer. Math. Soc. 149, 4973-4984 (2021), arXiv:1802.05894

• Applications of the hyperbolic Ax-Schanuel conjecture, with J. Ren, Compositio Mathematica, Volume 154, Issue 9, 1843-1888 (2018), arXiv:1703.08967

• The Zilber-Pink conjecture for pure Shimura varieties via o-minimality, in O-Minimality and its Applications to Number Theory and Analysis. Oberwolfach Rep. 14 (2017), no. 2, pp. 1349–1420, (open access version)

• Categoricity of modular and Shimura curves, with A. Harris, Journal of the Institute of Mathematics of Jussieu, Volume 16, Issue 5, 1075-1101 (2017), arXiv:1304.4797

• Heights of pre-special points of Shimura varieties, with M. Orr, Mathematische Annalen, Volume 365, Issue 3-4, 1305-1357 (2016), arXiv:1502.00822

• Degrees of strongly special subvarieties and the André-Oort conjecture, Journal fur die reine und angewandte Mathematik, Volume 2016, Issue 721, Pages 81-108

• The Andre-Oort conjecture via o-minimality, in O-minimality and Diophantine Geometry, edited by G.O. Jones and A.J. Wilkie, London Mathematical Society Lecture Note Series, Cambridge University Press, pp 129-158 (2015),  arXiv:1412.3237

• A simplified proof of the André-Oort conjecture for products of modular curves, Archiv der Mathematik, Volume 98, Issue 5, pp 433-440 (2012)

• On torsion of class groups of CM tori, Mathematika, Volume 58, Issue 02, pp. 305-318 (2012)

• An unconditional proof of the André-Oort conjecture for Hilbert modular surfaces, with A. Yafaev, Manuscripta Mathematica, Volume 135, Issue 1-2, pp 263-271 (2011)