Mathematics

This is Martin Bright's mathematical home page.

I am an associate professor (universitair hoofddocent) at 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.

Together with Valentijn Karemaker, Ronald van Luijk, Steffen Müller, Marta Pieropan and Cecília Salgado, I am part of the Rational Points consortium supported by an XL grant from the NWO.

Teaching

In 2023–24 I am teaching Lineaire Algebra 1 and the Mastermath course Advanced Algebraic Geometry: Rational Points (with Ronald van Luijk).

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

• 7–12 January 2024: New Directions in Rational Points, Chennai Mathematical Institute

Where I have been

• 11–15 September 2023: WAARP workshop, University of Bristol
• 25–29 April 2022: Rational Points on Higher-Dimensional Varieties, ICMS, Edinburgh
• 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

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.