Research

Papers:

• p-adic elliptic polylogarithms and cubic Chabauty (preprint). Joint with Jennifer Balakrishnan and Francesca Bianchi.

• 2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves II (preprint).

• The Zilber--Pink conjecture for products of curves with highly degenerate reduction (submitted).

• 2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves I (preprint).

• p-adic integrals and linearly dependent points on families of curves I (submitted).

• Quadratic Chabauty for modular curves: algorithms and examples (Compositio Mathematica, 2023). Joint with Jennifer Balakrishnan, Jan-Steffen Müller, Jan Tuitman and Jan Vonk.

• The Chabauty--Coleman method and p-adic linear forms in logarithms (preprint).

• The local structure of unipotent Kummer maps and refined Selmer schemes (submitted). Joint with Alex Betts.

• Quadratic Chabauty for modular curves and modular forms of rank one (Mathematische Annalen, 2020). Joint with Samuel Le Fourn.

• Unlikely intersections and the Chabauty--Kim method over number fields (Mathematische Annalen, 2023).

• An effective Chabauty--Kim theorem (Compositio Mathematica, 2019). Joint with Jennifer Balakrishnan.

• Explicit Chabauty-Kim for the split Cartan modular curve of level 13 (Annals of Mathematics, 2019). Joint with Jennifer Balakrishnan, Jan-Steffen Müller, Jan Tuitman and Jan Vonk.

• Quadratic Chabauty and rational points II: generalised height functions on Selmer varieties (International Mathematical Research Notices, 2020). Joint with Jennifer Balakrishnan.

• Quadratic Chabauty and rational points I: p-adic heights (Duke Mathematical Journal, 2018). Joint with Jennifer Balakrishnan, with appendix by Jan-Steffen Müller.

Other writing:

• Appendix to Ogg's Torsion conjecture: Fifty years later (Jennifer Balakrishnan and Barry Mazur)

• Topics in the Theory of Selmer Varieties (my thesis)