My research concerns problems related to the Birch and Swinnerton-Dyer conjecture, and its generalisation to abelian varieties. I am particularly interested in the parity conjecture, which asserts that the Birch and Swinnerton-Dyer conjecture correctly predicts the parity of the rank. With this in mind, I spend a lot of time trying to compute the parity of ranks of Jacobians of curves, using the arithmetic of curves over local fields.
My PhD thesis: The Parity Conjecture for Hyperelliptic Curves
Parity of ranks of Jacobians of curves, with V. Dokchitser, A. Konstantinou and A. Morgan. ArXiv:2211.06357.
The 2-parity conjecture for elliptic curves with isomorphic 2-torsion, with C. Maistret. Proceedings of the Royal Society A, 478.2265 (2022): 20220112.
Some codes in symmetric and linear groups, with M. W. Liebeck. Discrete Mathematics 343.8 (2020): 111719.
Parity conjecture for hyperelliptic curves: Elliptic Curves in the Cotswolds, The Cotswolds, 03/03/2025.
The Birch and Swinnerton-Dyer formula: Models of Curves Study Group, University of Bristol, 06/03/2024.
The Congruent Number Problem: Number Theory Day, University of Bristol, 24/01/2024.
On the parity conjecture for elliptic curves: Paris--London Number Theory Seminar, Université de Paris 8 & Université Sorbonne Paris Nord, 28/11/2023; Great Western Number Theory Seminar, University of Bath, 16/01/2024.
An arithmetic analogue of the parity conjecture: London Number Theory Seminar, University College London, 11/01/2023.
An introduction to root numbers and the parity conjecture: Galois Representations and Root Numbers Study Group, University College London, 15/11/2022.
A new rank parity computing machine: Mordell 2022: 100 years of elliptic curves, University of Cambridge, 16/08/2022.
Overview of function fields: Curves over Function Fields Study Group, University College London, 24/05/2022.
Parity of ranks of elliptic curves: Glasgow Algebra and Number Theory Seminar, University of Glasgow, 02/03/2022; London Junior Number Theory Seminar, King's College London, 22/03/2022; Linfoot Number Theory Seminar, University of Bristol, 30/03/2022.
The ring of integers of a function field and its primes: Function Fields Study Group, Online, 05/11/2021.
The Parity Conjecture for hyperelliptic curves: 'What have I been researching' Study Group, Online, 03/06/2021.
The Birch and Swinnerton--Dyer conjecture for curves: Curves Study Group, Online, 05/03/2021.
Parity of ranks of hyperelliptic curves: London Junior Number Theory Seminar, Online, 02/03/2021.
The Parity Conjecture: Birch and Swinnerton--Dyer Study Group, Online, 27/10/2020.
Understanding values of the Mobius function via root numbers: Bristol--London meeting, University College London, 06/12/2019.
Flat modules: Arithmetic Geometry Study Group, University College London, 28/11/2019.
The Congruent Number Problem: LSGNT Topics in Number Theory Wrap Up Session, King's College London, 26/11/2019.
The p-adic numbers: Introductory notes on the p-adic numbers, Imperial College London, 2018.
Elliptic Curves in the Cotswolds meeting: The Cotswolds, 03/03/2025--04/03/2025.
Linfoot Number Theory Seminar: University of Bristol, 2024--2025.
Women in Number Theory and Geometry Spring Retreat: Norfolk, 06/06/2022--08/06/2022.
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