Status:
Personal website:
ORCID iD:
https://orcid.org/0000-0002-3340-8868
Research groups:
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Highlighted Publications:
Cycles of covers
Monatshefte fur Mathematik
issue 3
volume 157
page 217-232
(1 July 2009)
Homogeneous spaces and degree 4 del Pezzo surfaces
Manuscripta Mathematica
issue 3
volume 129
page 369-380
(1 July 2009)
Nontrivial Sha in the Jacobian of an Infinite Family of Curves of Genus 2.
J. Theor. Nombres Bordeaux
volume 21
page 1-9
(1 April 2009)
Descent via isogeny on elliptic curves with large rational torsion subgroups
Journal of Symbolic Computation
issue 4
volume 43
page 293-303
(1 April 2008)
Two-coverings of Jacobians of curves of genus two
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY
volume 104
page 387-429
(February 2012)
Full text available
Recent Publications:
Arbitrarily large 2-torsion in Tate-Shafarevich groups of Abelian varieties
Acta Arithmetica
issue 2
volume 191
page 101-114
(5 September 2019)
Genus two isogeny cryptography
PQCrypto 2019: Post-Quantum Cryptography
volume 11505
page 286-306
(14 July 2019)
Arbitrarily large Tate–Shafarevich group on Abelian surfaces
Journal of Number Theory
volume 186
page 148-258
(16 November 2017)
Descent via (5,5)-isogeny on Jacobians of genus 2 curves
JOURNAL OF NUMBER THEORY
volume 153
page 270-282
(August 2015)
Full text available
Tight frames for cyclotomic fields and other rational vector spaces
LINEAR ALGEBRA AND ITS APPLICATIONS
volume 476
page 98-123
(1 July 2015)
Full text available
Research interests:
Number Theory, Arithmetic Geometry. In particular, arithmetic problems on Abelian varieties, such as Jacobians of curves; properties of the Shafarevich-Tate group, visualisation, and the Brauer-Manin obstruction.