During my PhD I worked on local-global principles, specifically the Hasse principle and weak approximation for norm and multinorm equations. In particular, I focused on combining algebraic techniques (such as Galois cohomology) with computational methods in GAP to study the validity and frequency of these principles in families.
Papers/Preprints
The Hasse norm principle for A_n extensions, Journal of Number Theory 211 (2020), 500-512. (journal, arXiv)
Explicit methods for the Hasse norm principle and applications to A_n and S_n extensions (joint with Rachel Newton), Mathematical Proceedings of the Cambridge Philosophical Society 172(3) (2022), 489-529. (journal, arXiv)
On the obstruction to the Hasse principle for multinorm equations, Israel Journal of Mathematics (2024), https://doi.org/10.1007/s11856-024-2689-7. (journal, arXiv)Â
PhD thesis
Local-global principles for norms, University of Reading, 2021.