Articles
See below for my mathematical articles.
- Lower Bounds for Counting A4-Quartic Fields, with Daniel Loughran, arXiv preprint, 2025
- Local Solubility of Generalised Fermat Equations, with Peter Koymans, Tim Santens, and Alec Shute, arXiv preprint, 2025
- Quadratic Twists as Random Variables, to appear in Transactions of the American Mathematical Society, arXiv preprint, 2024
- 2-Selmer Groups over Multiquadratic Extensions, arXiv preprint, 2024
- Conductors of Twisted Weil--Deligne Representations, with Matthew Bisatt, 2023, International Journal of Number Theory 21 (2025), no. 5, 975-991. arXiv preprint
- The Failure of Galois Descent for p-Selmer Groups of Elliptic Curves, Mathematical Proceedings of the Cambridge Philosophical Society 177 (2024), 185-218. arXiv preprint
- On 2-Selmer Groups of Twists after Quadratic Extension, with Adam Morgan, Journal of the London Mathematical Society 105 (2022), no. 2, 1110-1166. arXiv preprint.
Other
- From 13th-24th April 2026, Happy Uppal and I are hosting Peter Koymans at the University of Bristol via a Heilbronn International Visitors Scheme grant. During this visit, Peter will give a lecture series on the groundbreaking techniques of Alexander Smith. If you are non-Bristol-based and wish to travel here to attend, please contact us directly before making plans.
- From 2022 - 2025 I was an organiser for the Heilbronn Number Theory Seminar at the University of Bristol, details of the present organisers can be found on the seminar webpage.
- In September 2023, Julian Lyczak and I organised the workshop WAARP, which was held at the University of Bristol.
- In August 2022, Adam Morgan and I organised the fourth edition of Y-RANT, which was held at the University of Glasgow.
- A talk I gave at the Arithmetic Statistics and Local-Global Principles workshop, held at the ESI in Vienna in 2021, can be viewed here.
- My Ph.D. thesis, which won the William Jack prize 2022/23, can be found here.