I work on arithmetic and Diophantine geometry, including:
- Unlikely intersections in Shimura varieties, for example the André-Oort and Zilber-Pink conjectures.
- Arithmetic of abelian varieties and isogenies.
- The Mumford-Tate conjecture, linking the geometry and arithmetic of abelian varieties.
- Arithmetic and moduli of K3 surfaces.
Papers and preprints
Unlikely intersections with Hecke translates of a special subvariety
Finiteness theorems for K3 surfaces and abelian varieties of CM type
(with A. Skorobogatov)
to appear in Compositio Mathematica
Height bounds and the Siegel property
to appear in Algebra & Number Theory
On compatibility between isogenies and polarisations of abelian varieties
International Journal of Number Theory 13 (3), p. 673-704, 2017
Heights of pre-special points of Shimura varieties
(with C. Daw)
Mathematische Annalen 365 (3), p. 1305-1357, 2016
The proof of Lemma 2.15 in the published version of this paper is incorrect.
The correction can be found in the arXiv version of the paper.
Families of abelian varieties with many isogenous fibres
Journal für die reine und angewandte Mathematik 705, p. 211-231, 2015
There is a gap in the proof of Lemma 3.3 in the published version of this paper.
The gap was found and fixed by Gabriel Dill.
The corrections can be found in the arXiv version of the paper.
Lower bounds for ranks of Mumford-Tate groups
Bulletin de la Société Mathématique de France 143 (2), p. 229-246, 2015
Introduction to abelian varieties and the Ax-Lindemann-Weierstrass theorem
in O-minimality and Diophantine Geometry, edited by G. O. Jones and A. J. Wilkie, LMS Lecture Note Series 421, 2015
The André-Pink conjecture : Hecke orbits and weakly special subvarieties
(La conjecture d'André-Pink : orbites de Hecke et sous-variétés faiblement spéciales)
PhD thesis, Université Paris Sud, 2013
Errata for my thesis