Research
Publications & Preprints
Computing Euler Factors of genus 2 curves at odd primes of almost good reduction, with A. Sutherland (arXiv:2402.02271)
2-parity conjecture for elliptic curves with isomorphic 2-torsion, with H. Green. Proceedings of the Royal Society A (arXiv 2110.06718)
A user's guide to the local arithmetic of hyperelliptic curves, with A. J. Best, L. A. Betts, M. Bisatt, R. van Bommel, V. Dokchitser, O. Faraggi, S. Kunzweiler, A. Morgan, S. Muselli, S. Nowell. Bulletin of the London Mathematical Society. (arXiv:2007.01749)
On the parity conjecture for abelian surfaces, with V. Dokchitser, Proceedings of the London Mathematical Society ( arXiv:1911.04626)
Arithmetic of hyperelliptic curves over local fields, with T. Dokchitser, V. Dokchitser, A. Morgan. Mathematische Annalen. (arXiv:1808.02936)
Semistable types of hyperelliptic curves, with T. Dokchitser, V. Dokchitser, A. Morgan. Contemporary Mathematics, Volume 724, (2019).
Elliptic fibrations on covers of the elliptic modular surface of level 5, with F. Balastrieri, J. Desjardins, A. Garbagnati, C. Salgado and I. Vogt. WINE II: Contributions to Number Theory and Arithmetic Geometry, AWM Springer Series 11 (2018)
Parity of ranks of Jacobians of hyperelliptic curves of genus 2, PhD thesis.
Birch and Swinnerton-Dyer conjecture for elliptic curves over pure cubic extensions, Master's thesis.
PhD students
Don't hesitate to get in touch to discuss possible PhD projects if you are interested in computational number theory and arithmetic geometry, in particular the arithmetic of elliptic and hyperelliptic curves, the Birch--Swinnerton-Dyer conjecture and the parity conjecture.