Research
Research
My research is at the interface of arithmetic geometry and model theory. I am interested in applications of model-theoretic methods (in particular, o-minimality and differential algebra) to questions in Diophantine geometry. Much of my work falls into the area of "unlikely intersections", which encompasses questions generalising classical Diophantine results like Faltings's theorem (the Mordell conjecture) on the finiteness of rational points on curves of genus at least 2. I am especially interested in aspects relating to uniformity and effectivity for such questions.
Full details of my publications and preprints are below. The most recent arXiv versions of my published papers are identical with the published versions in terms of content and numbering of theorems etc.
André's theorem via weakly bounded height. (2026).
Modular Zilber--Pink for geometrically generic varieties. With Vahagn Aslanyan and Sebastian Eterović (2025).
Distinct differences of singular moduli. With Emanuele Tron (2025).
[ArXiv version] [PARI scripts]
Some uniform effective results on André--Oort for sums of powers in C^n. (2024). Math. Proc. Camb. Philos. Soc. 180 (2026), no. 3, 607-641.
[Journal version] [ArXiv version] [PARI scripts]
Multiplicative relations among differences of singular moduli. With Vahagn Aslanyan and Sebastian Eterović (2023). To appear in Ann. Sc. Norm. Super. Pisa Cl. Sci.
[Journal version] [ArXiv version]
Equations in three singular moduli: the equal exponent case. J. Number Theory 243 (2023), 256-297.
[Journal version] [ArXiv version] [PARI scripts]
Multiplicative independence of modular functions. J. Théor. Nombres Bordeaux 33 (2021), no. 2, 459-509.
[Journal version] [ArXiv version]
Triples of singular moduli with rational product. Int. J. Number Theory 16 (2020), no. 10, 2149-2166.
[Journal version] [ArXiv version] [PARI scripts]
Multiplicative relations among special points of modular and Shimura curves. University of Oxford, 2021.