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Research Interests


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


Publications and Preprints


Parity of ranks of Jacobians of curves, with V. Dokchitser, A. Konstantinou and A. Morgan. Proceedings of the London Mathematical Society (to appear).


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.


Talks and Notes


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.


Organisation


Elliptic Curves in the Cotswolds meeting: The Cotswolds, 03--04/03/2025.


Linfoot Number Theory Seminar: University of Bristol, 2024--2025.


Women in Number Theory and Geometry Spring Retreat: Norfolk, 06--08/06/2022.

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