Mathematics

This is Martin Bright's mathematical home page.

I am a member of the Mathematisch Instituut at the University of Leiden in the Netherlands. I work in the area of Diophantine equations and arithmetic geometry, specifically on the Brauer–Manin obstruction and related questions about rational points on varieties.

Teaching

In 2021–22 I am teaching Lineaire Algebra 1 and the Mastermath course Elliptic Curves (with Valentijn Karemaker).

Lecture notes: Descent by 2-isogeny (following Cassels). (Corrections welcome!)

Articles

Here is a list of my publications and preprints, together with slides from some talks.

Notes from the Autumn School in Mainz, October 2017 are available here.

Look me up on Google Scholar or MathSciNet.

Book

Conferences and workshops

Where I will be

• 25–29 April 2022: Rational Points on Higher-Dimensional Varieties, ICMS, Edinburgh

Where I have been

• 20–24 September 2021: Arithmetic Statistics and Local-Global Principles, Erwin Schrödinger Institute, Vienna
• 17–19 May 2021: Memorial conference for Sir Peter Swinnerton-Dyer, Newton Institute, Cambridge
• 21 March–30 April 2021: Programme on Number Theory, Institut Mittag-Leffler, Djursholm
• 14–20 July 2019: Rational Points 2019, Schney, Germany
• 29 April–12 July 2019: À la Redécouverte des Points Rationnels, Institut Henri Poincaré, Paris
• 2–6 July 2018: Rational Points on Schiermonnikoog, Schiermonnikoog, Netherlands
• 28 May–1 June 2018: Rational and Integral Points via Analytic and Geometric Methods, Oaxaca, Mexico
• 7–11 May 2018: An Algebraic Approach to Multilinear Maps for Cryptography, Banff, Canada
• 2–4 May 2018: K3 surfaces and Galois representations, Shepperton, UK
• 23–27 October 2017: Constructing cryptographic multilinear maps, AIM, San José, California, USA
• 9–13 October 2017: Topics in Arithmetic and Algebraic Geometry, Mainz, Germany
• 11–15 September 2017: Diophantine Problems (DIOP), Manchester, UK
• 3–7 July 2017: Rational Points 2017, Schney, Germany
• 7–9 June 2017: Journées Algophantiennes Bordelaises 2017, Bordeaux, France
• 26–30 September 2016: Rational Points and Algebraic Geometry, CIRM, Luminy, France
• 4–8 April 2016: Explicit Methods in Number Theory: conference in honour of John Cremona's 60th birthday, Warwick, UK

Things I have organised

• In July 2018, Jan Steffen Müller, Damaris Schindler, Arne Smeets and I organised Rational Points on Schiermonnikoog.
• From September 2016 to July 2019, Peter Bruin and I organised the Leiden algebra, geometry and number theory seminar.
• From Easter 2010 to summer 2011 I organised the Warwick number theory seminar.
• Ronald van Luijk, Damiano Testa and I gave an instructional workshop on the geometry and arithmetic of surfaces at Warwick in April 2008, organised by Samir Siksek and ourselves.
• Tim Browning and I organised Diophantine Equations via Analytic Number Theory (DEViANT), 9–12 July 2007, Bristol.

Other resources

My PhD research (2002) involved doing some computations on diagonal quartic surfaces. Here are some bits of code and results.