(with Adam Logan and Ronald van Luijk) Finiteness theorems for K3 surfaces over arbitrary fields. (arXiv:1810.04905)

(with Julian Lyczak) A uniform bound on the Brauer groups of certain log K3 surfaces.
*Michigan Mathematical Journal*, to appear.
(article
arXiv:1705.04529)

(with Ivo Kok) Failure of strong approximation on an affine cone.
*Involve, a Journal of Mathematics*, volume 12(2), 2019, pp. 321–327.
(article
arXiv:1707.04177)

Obstructions to the Hasse principle in families.
*Manuscripta Mathematica*, volume 157(3), 2018, pp. 529–550.
(article
PDF
arXiv:1607.01303)

(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[2]. *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)

A uniform bound on the Brauer groups of certain log K3 surfaces. Video of talk at Casa Matemática Oaxaca, 31 May 2018.

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.

Martin Bright

Last modified: 20 October 2018