Peter Bruin

Picture of Peter Bruin

CV

October 2011–present	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, Département de Mathématiques d'Orsay, Université Paris-Sud 11
September 2006–September 2010	Promovendus, Mathematisch Instituut, Universiteit Leiden

Publications

Merkl's method of bounding Green functions. Appendix to: A. Javanpeykar, Polynomial bounds for Arakelov invariants of Belyi curves. Algebra & Number Theory, to appear. PDF.
With J. G. Bosman, A. Dujella and F. Najman: Ranks of elliptic curves with prescribed torsion over number fields. International Mathematical Research Notices, electronically published on 15 February 2013. IMRN.
Computing in Picard groups of projective curves over finite fields. Mathematics of Computation 82 (2013), 1711–1756. AMS, PDF (version of 15 October 2011).
The Tate pairing for Abelian varieties over finite fields. Journal de théorie des nombres de Bordeaux 23 (2011), no. 2, 323–328. CEDRAM, PDF.
Computing coefficients of modular forms. Publications mathématiques de Besançon, année 2011 (actes de la conférence Théorie des nombres et applications, CIRM, Luminy, 30 novembre–4 décembre 2009), 19–36. PDF (published version).

Prepublications/Protopublications

With F. Najman: The growth of the rank of Abelian varieties upon extensions. Submitted. arXiv preprint.
Explicit bounds on automorphic and canonical Green functions of Fuchsian groups. Submitted. PDF (version of 4 February 2013). (Supersedes two preprints: An approximate spectral representation and explicit bounds for Green functions of Fuchsian groups and Explicit bounds on canonical Green functions of modular curves.)
Bornes optimales pour la différence entre la hauteur de Weil et la hauteur de Néron–Tate sur les courbes elliptiques sur Q. Submitted. arXiv preprint, PARI/GP script (from source package on arXiv).
An algorithm for computing modular Galois representations. In preparation.

Sage Days, 22–26 July 2013

Together with Maarten Derickx and Michiel Kosters, I am organising an edition of the Sage Days, to be held in the Lorentz Center in Leiden, 22–26 July 2013. The workshop is titled Algorithms in Arithmetic Geometry. Further information will appear in due course on the workshop webpage and on wiki.sagemath.org/sagedaysleiden.

Lehre | Teaching

Lineare Algebra und Geometrie (Assistent), Herbstsemester 2012
Elliptische Kurven (Assistent), Frühjahrssemester 2012
Studentenseminar Elliptische Funktionen und Modulformen (Organisator), Herbstsemester 2011

Proefschrift | Ph. D. thesis

Modular curves, Arakelov theory, algorithmic applications (PDF, PS)
Stellingen (propositions, in Dutch; PDF, PS)
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 (PDF, PS)
Universiteit Leiden, 28 June 2006
Supervised by Prof. dr. S. J. Edixhoven and Dr. R. S. de Jong

Notes of talks

What is… an L-function? Zurich Graduate Colloquium, 30 October 2012
Optimal bounds for the difference between the Néron–Tate height and the Weil height on elliptic curves over Q, Selmer Groups, Descent and the Distribution of Ranks, University of Warwick, 28 September 2012
Modular curves and Galois representations, mini-course given at the workshop Modular Forms and Related Topics II, CAMS, American University of Beirut, 6–10 February 2012
Groupes de Chow supérieurs, applications classe de cycle et régulateurs étales, groupe de travail Zéro-cycles sur les variétés p-adiques, ENS Paris, 9 février 2011
Calcul de coefficients de formes modulaires, séminaire d'arithmétique et de géometrie algébrique, Orsay, 25 janvier 2011
Computing coefficients of modular forms, Théorie des nombres et applications, CIRM, Luminy (Marseille), 30 November 2009
Arakelov theory and height bounds, Forschungsseminar Arithmetische Geometrie, Humboldt-Universität zu Berlin, 17 November 2009
Computing in Picard groups of projective curves over finite fields, Arbeitsgemeinschaft Zahlentheorie, Institut für Experimentelle Mathematik, Universität Duisburg–Essen, 10 November 2009
Endomorphism rings of Abelian varieties and their representations, seminar on complex multiplication for Abelian varieties, 14 October and 11 November 2009
Global class field theory, seminar on adelic methods, 6 October 2008
Explicit towers of curves with many points, seminar on rational points on curves over finite fields, 25 April 2008, and DIAMANT/EIDMA symposium, Oegstgeest, 29 May 2008
Moduli of elliptic curves, seminar on moduli spaces and modular forms, 12 September 2007
Sketch of a construction of the Néron model of an Abelian variety, seminar on Néron models, 4 April 2007
Smooth morphisms, seminar on Néron models, 21 February 2007
Formal groups, seminar on complex multiplication, 2 March 2006
Curves in P¹ × P¹, seminar on cohomology of quasi-coherent sheaves, 16 November 2005
Kolmogorov–Arnold–Moser theory, Classical Mechanics and Dynamical Systems, 16 November 2004
De kubus van Rubik, studentenseminarium, 11 maart 2004

Last modified on 22 April 2013.