Professor 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
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)
Explicit $n$-descent on elliptic curves III. Algorithms
– Mathematics of Computation
(2012)
84,
895
Local solubility and height bounds for coverings of elliptic curves
– Mathematics of Computation
(2012)
81,
1635
The Hessian of a genus one curve
– Proceedings of the London Mathematical Society
(2011)
104,
613
(doi: 10.1112/plms/pdr039)
The yoga of the Cassels-Tate pairing
– LMS Journal of Computation and Mathematics
(2010)
13,
451
(doi: 10.1112/s1461157010000185)
Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves
– Algebra & Number Theory
(2010)
4,
763
(doi: 10.2140/ant.2010.4.763)
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