Peter Bruin

Contact

Contact information

Publications

• Computing in Picard groups of projective curves over finite fields. Mathematics of Computation, to appear. 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).

Preprints

• With J. Bosman, A. Dujella and F. Najman: Ranks of elliptic curves with prescribed torsion over number fields. Submitted. arXiv preprint.
• Explicit bounds on Green functions of Fuchsian groups. In preparation.

Lehre | Teaching

Universität Zürich

• Elliptische Kurven (Assistent), Frühjahrssemester 2012
• Studentenseminar Elliptische Funktionen und Modulformen, Herbstsemester 2011

Universiteit Leiden

• Algebra 3 (assistent), voorjaar 2010
• Lineaire algebra 2 (assistent), najaar 2009
• Seminar on complex multiplication for Abelian varieties, with Marco Streng, autumn 2009
• Algebra 3 (assistent), voorjaar 2009
• Algebra 2 (assistent), najaar 2008
• Seminar on adelic methods, with Arjen Stolk, autumn 2008
• Elliptic curves (assistant), spring 2008
• Seminar on rational points on curves over finite fields, with Arjen Stolk, spring 2008
• Lineaire algebra 2 (assistent), najaar 2007
• Seminar on moduli spaces and modular forms, with Marco Streng, autumn 2007
• Algebraic geometry (assistant), spring 2007
• Seminar on Néron models, spring 2007

Proefschrift | Ph. D. thesis

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

Notes of talks

• 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 28 January 2012.