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
HIGHER DESCENTS ON AN ELLIPTIC CURVE WITH A RATIONAL 2-TORSION POINT
– Mathematics of Computation
(2017)
86,
2493
(doi: 10.1090/mcom/3163)
On genus one curves of degree 5 with square-free discriminant
– JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY
(2016)
31,
359
Visualizing elements of order $7$ in the Tate–Shafarevich group of an elliptic curve
– LMS Journal of Computation and Mathematics
(2016)
19,
100
(doi: 10.1112/S1461157016000243)
The proportion of plane cubic curves over ℚ that everywhere locally have a point
– International Journal of Number Theory
(2016)
12,
1077
(doi: 10.1142/S1793042116500664)
What is the Probability that a Random Integral Quadratic Form in n Variables 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. Algèbre et théorie des nombres
(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)
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