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
Explicit n-descent on elliptic curves, II. Geometry
– Journal für die reine und angewandte Mathematik (Crelles Journal)
(2009)
632,
63
(doi: 10.1515/CRELLE.2009.050)
On the equivalence of binary quartics
– Journal of Symbolic Computation
(2009)
44,
673
(doi: 10.1016/j.jsc.2008.09.004)
Finding rational points on elliptic curves using 6-descent and 12-descent
– Journal of Algebra
(2008)
320,
853
The invariants of a genus one curve
– Proceedings of the London Mathematical Society
(2008)
97,
753
(doi: 10.1112/plms/pdn021)
Explicit n-descent on elliptic curves, I. algebra
– Journal für die reine und angewandte Mathematik (Crelles Journal)
(2008)
2008,
121
(doi: 10.1515/crelle.2008.012)
Some improvements to 4-descent on an elliptic curve
– ALGORITHMIC NUMBER THEORY
(2008)
5011,
125
A new approach to minimising binary quartics and ternary cubics
– Mathematical Research Letters
(2007)
14,
597
(doi: 10.4310/mrl.2007.v14.n4.a5)
Testing equivalence of ternary cubics
– ALGORITHMIC NUMBER THEORY, PROCEEDINGS
(2006)
4076,
333
Root Numbers of Non‐Abelian Twists of Elliptic Curves
– Proceedings of the London Mathematical Society
(2005)
91,
300
(doi: 10.1112/S0024611505015261)
Descent Calculations for the Elliptic Curves of Conductor 11
– Proceedings of the London Mathematical Society
(2003)
86,
583
(doi: 10.1112/S0024611502013977)
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