Reader 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
What is the Probability that a Random Integral Quadratic Form innVariables has an Integral Zero?
– International Mathematics Research Notices
(2015)
2016,
3828
(DOI: 10.1093/imrn/rnv251)
Ranks of quadratic twists of elliptic curves
– Publications Mathématiques de Besançon
(2015)
63
(DOI: 10.5802/pmb.9)
On families of 9-congruent elliptic curves
– Acta Arithmetica
(2015)
171,
371
(DOI: 10.4064/aa171-4-5)
Computing the Cassels-Tate pairing on the 3-Selmer group of an elliptic curve
– International Journal of Number Theory
(2014)
10,
1881
(DOI: 10.1142/s1793042114500602)
On families of 7- and 11-congruent elliptic curves
– LMS Journal of Computation and Mathematics
(2014)
17,
536
(DOI: 10.1112/S1461157014000059)
Minimal models for $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}6$-coverings of elliptic curves
– LMS Journal of Computation and Mathematics
(2014)
17,
112
(DOI: 10.1112/S1461157014000217)
Minimisation and reduction of 5-coverings of elliptic curves
– Algebra & Number Theory
(2013)
7,
1179
(DOI: 10.2140/ant.2013.7.1179)
Invisibility of Tate–Shafarevich Groups in Abelian Surfaces
– International Mathematics Research Notices
(2013)
2014,
4085
(DOI: 10.1093/imrn/rnt068)
Explicit 5-descent on elliptic curves
(2013)
Invariant theory for the elliptic normal quintic, I. Twists of X(5)
– Mathematische Annalen
(2012)
356,
589
(DOI: 10.1007/s00208-012-0850-9)
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