Back to my mathematics page
(with Ivo Kok) Failure of strong approximation on an affine cone. Involve, to appear. (arXiv:1707.04177)
Obstructions to the Hasse principle in families. Manuscripta Mathematica, to appear. (article arXiv:1607.01303)
(with Julian Lyczak) A uniform bound on the Brauer groups of certain log K3 surfaces. Michigan Mathematical Journal, to appear. arXiv:1705.04529
(with Tim Browning and Dan Loughran) Failures of weak approximation in families. Compositio Mathematica, volume 152(07), 2016, pp. 1435–1475. (arXiv:1506.01817 article)
Bad reduction of the Brauer–Manin obstruction. J. London Math. Soc., volume 91(3), 2015, pp. 643–666. (article arXiv:1309.2488)
Brauer groups of singular del Pezzo surfaces. Michigan Mathematical Journal, volume 62(3), 2013, pp. 657–664. (article arXiv:1201.4299)
Torsors under tori and Néron models. Journal de Théorie des Nombres de Bordeaux, volume 23(2), 2011, pp. 309–321. (article arXiv:0911.4834)
The Brauer–Manin obstruction on a general diagonal quartic surface. Acta Arithmetica, volume 147(3), 2011, pp. 291–302. (article arXiv:1008.0999)
Evaluating Azumaya algebras on cubic surfaces. Manuscripta Mathematica, volume 134(3), 2011, pp. 405–421. (article arXiv:0810.3535)
(with Samir Siksek) Functions, reciprocity and the obstruction to divisors on curves. J. London Math. Soc., volume 77(3), 2008, pp. 789–807. (article)
(with Nils Bruin, Victor Flynn and Adam Logan) The Brauer–Manin obstruction and Sha. LMS J. Comput. Math., volume 10, 2007, pp. 354–377. (article)
Efficient evaluation of the Brauer–Manin obstruction. Math. Proc. Camb. Phil. Soc., volume 142(1), 2007, pp. 13–23. (Journal DVI PDF)
Brauer groups of diagonal quartic surfaces. J. Symbolic Computation, volume 41, 2006, pp. 544–558. (Journal DVI PDF)
(with Sir Peter Swinnerton-Dyer) Computing the Brauer–Manin obstructions. Math. Proc. Camb. Phil. Soc., volume 137 (2004), pp. 1–16. (Journal DVI PDF)
Rational points in families of varieties. Lecture notes from my lecture course at Topics in Arithmetic and Algebraic Geometry, Mainz, Germany, October 2017.
Failures of weak approximation in families. Video of talk at IMPA, Rio de Janeiro, May 2015.
Brauer–Manin obstructions on general diagonal quartic surfaces. Slides from talk, Arithmetic of Surfaces, Lorentz Center, Leiden, October 2010. (PDF).
Computing Brauer–Manin obstructions on diagonal quartic surfaces. Slides from talk, Arithmetic of K3 surfaces, Banff, December 2008. (PDF). Also available: Magma code.
Efficient computation of the Brauer–Manin obstruction. Slides from seminar, Explicit Arithmetic Geometry workshop, Institut Henri Poincaré, Paris, December 2004. (DVI PDF)
Computing Galois groups by specialisation. Poster at ANTS VI, University of Vermont, June 2004. (DVI PDF) Condensed version in SIGSAM bulletin Communications in Computer Algebra, volume 38, no. 3 (September 2004).
Computations on diagonal quartic surfaces. PhD thesis, University of Cambridge, 2002.
(with Joan Mitchell) Reduced-error processing of transformed digital data. US patent no. 7,194,138 (20 March, 2007). full text.
(with Joan Mitchell) Error reduction in transformed digital data. US patent nos. 6,393,155 (21 May, 2002) (full text) and 6,535,645 (18 March, 2003) (full text).
(with Joan Mitchell) Transform-domain correction of real-domain errors. US patent no. 6,256,422 (3 July, 2001). full text.