Articles

See below for my mathematical articles.

• Lower Bounds for Counting A_4-Quartic Fields, with Daniel Loughran, 2025.  Abstract, arXiv preprint.
• Local Solubility of Generalised Fermat Equations, with Peter Koymans, Tim Santens, and Alec Shute, 2025.  Abstract, arXiv preprint.
• Quadratic Twists as Random Variables, to appear in Transactions of the American Mathematical Society, 2024.  Abstract, arXiv preprint.
• 2-Selmer Groups over Multiquadratic Extensions, 2024.  Abstract, arXiv preprint.
• Conductors of Twisted Weil--Deligne Representations, with Matthew Bisatt, International Journal of Number Theory 21 (2025), no. 5, 975-991.  Abstract, 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.  Abstract, 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.  Abstract, arXiv preprint.

Other

• In April 2026, Happy Uppal and I hosted Peter Koymans at the University of Bristol via a Heilbronn International Visitors Scheme grant.  The website for Peter's lecture series is here
• 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.