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
Explicit moduli spaces for congruences of elliptic curves
– Mathematische Zeitschrift
(2019)
1
(DOI: 10.1007/s00209-019-02392-9)
On some algebras associated to genus one curves
– Journal of Algebra
(2019)
518,
519
Some minimisation algorithms in arithmetic invariant theory
– Journal de Theorie des Nombres de Bordeaux
(2018)
30,
801
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)
A formula for the Jacobian of a genus one curve of arbitrary degree
– Algebra & Number Theory
(2018)
12,
2123
(DOI: 10.2140/ant.2018.12.2123)
Higher descents on an elliptic curve with a rational 2-torsion point
– Mathematics of Computation
(2016)
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
(2016)
2016,
3828
(DOI: 10.1093/imrn/rnv251)
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