Peter Bruin

Picture of Peter Bruin

Universitair docent (assistant professor), Mathematisch Instituut, Universiteit Leiden

I am affiliated with the Quantum Software Consortium, an NWO Gravitation project.

Universiteit Leiden
Mathematisch Instituut
Postbus 9512
2300 RA Leiden

Mathematisch Instituut
Gorlaeusgebouw, kamer BW.2.19
Einsteinweg 55
2333 CC Leiden

Telephone: (+31) 71 527 7142

Onderwijs | Teaching


(Published versions differ slightly from preprints.)


Mathematical software

For my research, I often use the free* mathematical software systems PARI/GP and SageMath. I regularly contribute to SageMath by adding new features, fixing bugs and improving existing code. I have also made a number of contributions to PARI/GP.

* Free as in "free speech", not only as in "free beer"; see the GNU project.

The abgalrep, ellgalrep and modgalrep packages

I have written three software packages for computing Galois representations (or finite commutative group schemes over Q) attached to arithmetic objects:

Note: modgalrep is by far the largest of these packages; it consists of a C program together with several libraries and GP scripts. The other two are smaller and just consist of GP scripts.

The dual-pairs package

This is a SageMath package for computing with finite commutative group schemes and Galois representations in the form of dual pairs of algebras, as described in the preprint Dual pairs of algebras and finite commutative group schemes.

Agda packages

These are formalisations of small parts of mathematics in dependent type theory using the the Agda programming language.


An Expedition into Arithmetic Geometry (2023)

Together with Samuele Anni, Hélène Esnault, Ronald van Luijk, Pierre Parent, Gabor Wiese and Andrei Yafaev, I organised the workshop An Expedition into Arithmetic Geometry, held in memory of Bas Edixhoven at the Lorentz Center (Leiden) from 30 May to 2 June 2023. The concluding event was the Bas Edixhoven Memorial Symposium on the afternoon of Friday 2 June.

COUNT workshop (2023)

I was one of the organisers of the workshop COUNT (COmputations and their Uses in Number Theory) at CIRM (Marseille) from 27 February to 3 March 2023.

6th QSC General Assembly (2021)

Wolfgang Löffler and I organised the 6th General Assembly of the Quantum Software Consortium at the Universiteit Leiden on Friday 5 November 2021.

Algorithms in Number Theory and Arithmetic Geometry (2017)

I organised the workshop Algorithms in Number Theory and Arithmetic Geometry at the Universiteit Leiden from 31 July to 4 August 2017.

Sage Days 51: Algorithms in Arithmetic Geometry (2013)

Together with Maarten Derickx and Michiel Kosters, I organised an edition of the Sage Days, titled Algorithms in Arithmetic Geometry, in the Lorentz Center in Leiden, 22–26 July 2013. See also the wiki.

Previous positions

October 2018 Guest, Max-Planck-Institut für Mathematik, Bonn
September 2013-August 2014 Assistant professor (Warwick Zeeman Lecturer), Mathematics Institute, University of Warwick
October 2011–August 2013 Postdoc, Institut für Mathematik, Universität Zürich
June–July 2012 Guest, Max-Planck-Institut für Mathematik, Bonn
August–September 2011 Visiteur, Institut des Hautes Études Scientifiques, Bures-sur-Yvette
October 2010–July 2011 Postdoc, Laboratoire de Mathématiques d'Orsay, Université Paris-Sud 11
September 2006–September 2010 Promovendus, Mathematisch Instituut, Universiteit Leiden

Proefschrift | Ph. D. thesis

Modular curves, Arakelov theory, algorithmic applications
Stellingen (propositions, in Dutch)
Universiteit Leiden, 1 September 2010
Promotor: Prof. dr. S. J. Edixhoven
Copromotor: Dr. R. S. de Jong

Doctoraalscriptie | Master's thesis

Green functions on Riemann surfaces and an application to Arakelov theory
Universiteit Leiden, 28 June 2006
Supervised by Prof. dr. S. J. Edixhoven and Dr. R. S. de Jong

Notes of talks

Laatste wijziging: 13 juli 2024.