Research

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

1. The Hasse norm principle for A_n extensions, Journal of Number Theory 211 (2020), 500-512. (journal, arXiv)

2. Explicit methods for the Hasse norm principle and applications to A_n and S_n extensions (joint with Rachel Newton), to appear in Mathematical Proceedings of the Cambridge Philosophical Society. (journal, arXiv)

3. On the obstruction to the Hasse principle for multinorm equations, to appear in Israel Journal of Mathematics. (arXiv)

4. A note on the density of D_4-fields failing the Hasse norm principle, in preparation.

PhD thesis

Local-global principles for norms, University of Reading, 2021.