Professor (Grade 11) in Number Theory
Research Interests: My research interests are in arithmetical algebraic geometry and computational number theory. In particular I work on elliptic curve descent calculations, and the construction of explicit elements in the Tate-Shafarevich group.
Publications
On binary quartics and the Cassels-Tate pairing
– Research in Number Theory
(2022)
8,
74
(doi: 10.1007/s40993-022-00376-z)
The density of polynomials of degree n$n$ over Zp${\mathbb {Z}}_p$ having exactly r$r$ roots in Qp${\mathbb {Q}}_p$
– Proceedings of the London Mathematical Society
(2022)
124,
713
(doi: 10.1112/plms.12438)
Everywhere local solubility for hypersurfaces in products of projective spaces
– Research in Number Theory
(2021)
7,
6
(doi: 10.1007/s40993-020-00223-z)
The proportion of genus one curves over Q defined by a binary quartic that everywhere locally have a point
– International Journal of Number Theory
(2020)
17,
903
(doi: 10.1142/S1793042121500147)
Explicit moduli spaces for congruences of elliptic curves
– Mathematische Zeitschrift
(2019)
295,
1337
(doi: 10.1007/s00209-019-02392-9)
Some minimisation algorithms in arithmetic invariant theory
– Journal de Théorie des Nombres de Bordeaux
(2019)
30,
801
(doi: 10.5802/jtnb.1050)
On some algebras associated to genus one curves
– Journal of Algebra
(2019)
518,
519
Visibility of 4-covers of elliptic curves
– Research in Number Theory
(2018)
4,
11
(doi: 10.1007/s40993-018-0106-1)
A formula for the Jacobian of a genus one curve of arbitrary degree
– Algebra and Number Theory
(2018)
12,
2123
(doi: 10.2140/ant.2018.12.2123)
Computing the Cassels-Tate pairing on 3-isogeny Selmer groups via cubic norm equations
– Acta Arithmetica
(2018)
185,
367
(doi: 10.4064/aa171108-11-4)
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