René Pannekoek

I am a PhD student (Dutch: promovendus) in my final year. I am in the research group Number Theory and Algebra. My research interest is rational points on varieties, in particular the arithmetic of K3 surfaces. Among other things, I have studied the density of rational points in the p-adic topology on diagonal quartic surfaces and Kummer surfaces.

Contact

Office: Snellius building, room 231

Postal address: PO Box 9512, 2300 RA Leiden

Visiting address: Niels Bohrweg 1, 2333 CA Leiden

Telephone: 071-5277131 / +31-71-5277131

E-mail: my first name at math dot leidenuniv dot nl

Preprints

(With David Holmes.) Distributions of rational points on Kummer varieties (arXiv).
On p-adic density of rational points on K3 surfaces (arXiv).
On p-torsion of p-adic elliptic curves with additive reduction (arXiv).

Teaching

Algebra 3 (Spring 2013)
Lineaire Algebra 1 voor Natuur- en Sterrenkundigen (Fall 2012)
Algebra 1 (Spring 2012)
Elliptic Curves (MasterMath) (Fall 2011)
Algebra 3 (Spring 2011)
Algebra 2 (Fall 2010)
Algebra 1 (Spring 2010)
Elliptic Curves (MasterMath) (Fall 2009)

Current & upcoming events

Documents

My master's thesis, entitled "Parametrizations over Q of cubic surfaces". Its subject is cubic surfaces in P³. In chapter 2, some of the classically known facts about smooth cubic surfaces are explained.
My bachelor's thesis (Dutch), entitled "MDS-codes en AMDS-codes afkomstig van algebraïsche krommen van geslacht nul en één".

Talks

Surfaces and numbers (English slides, Dutch slides). Nederlands Mathematisch Congres, Nijmegen, 5 April 2013.
On p-adic density of rational points on K3 surfaces. Heilbronn Seminar, Bristol University, 6 February 2013.
Explicit unbounded ranks of Jacobians of higher genus curves in towers of function fields (slides). DIAMANT Symposium, Doorn, 29/30 November 2012.
Introduction to Hodge Theory. Seminar on Deligne's proof of the Weil conjecture for K3 surfaces, Leiden University, 6 November 2012.
Introduction to K3 surfaces. Seminar on Deligne's proof of the Weil conjecture for K3 surfaces, Leiden University, 30 October 2012.
On p-adic density of rational points on K3 surfaces. RatPAC seminar in Lausanne (part of a semester on Rational Points and Algebraic Cycles), EPFL, 26 July 2012.
Dedekind domains and discrete valuation rings. Seminar on Commutative Algebra, Leiden University, 12 April 2012.
On p-adic density of rational points on K3 surfaces (abstract). London Number Theory Seminar, Imperial College, London, 7 March 2012.
On p-adic density of rational points on K3 surfaces (abstract). Algebra, geometry and number theory seminar, Leiden University, 27 February 2012.
The group law on elliptic curves over an arbitrary base scheme II. Seminar "Topics in Algebraic Geometry", Leiden University, 27 February 2012.
The group law on elliptic curves over an arbitrary base scheme I. Seminar "Topics in Algebraic Geometry", Leiden University, 13 February 2012.
A question about elliptic curves over finite fields (pdf). Elliptic Curves, Vrije Universiteit Amsterdam, 13 December 2011.
Pontryagin Duality. Seminar "Fourier Analysis on Number Fields", Leiden, 31 October 2011.
Topological groups and Haar measures. Seminar "Fourier Analysis on Number Fields", Leiden, 12 September 2011.
The work of Skorobogatov and Zarhin on Brauer groups of Kummer surfaces. Seminar on Étale Cohomology, Leiden, 21 June 2011.
On p-adic density of rational points on certain K3 surfaces (pdf). DIAMANT/EIDMA Symposium, Heeze, 27 May 2011.
Fpqc sheaves and fpqc descent. Seminar on Étale Cohomology, Leiden, 8 March 2011.
The fpqc site. Seminar on Étale Cohomology, Leiden, 1 March 2011.
Kwadratische reciprociteit (pdf). Bachelorseminarium, University of Leiden, 9 February 2011.
Elliptische krommen in de p-adische topologie (abstract, voordracht). Bachelorseminarium, Leiden, 25 January 2011.
Het verdelen van een vierkant in driehoeken van gelijke oppervlakte (pdf). Algebra 2, Leiden, 15 December 2010.
Diagonal quartic surfaces in the p-adic topology (pdf). DIAMANT/EIDMA Symposium, Lunteren, 26 November 2010.
Lubin-Tate theory. Seminar on class field theory, University of Leiden, 24 November 2010.
The local Artin map for Q_p. Seminar on class field theory, University of Leiden, 17 November 2010.
The Brauer group of a field. Seminar on obstructions, University of Leiden, 29 June 2010.
The descent obstruction (pdf). Seminar on obstructions, University of Leiden, 23 June 2010.
De gulden snede (pdf). Gastles, Pallas Athene College, Ede, 29 April 2010.
The Castelnuovo Rationality Criterion. Seminar on Algebraic Surfaces, University of Leiden, 26 April 2010.
Ruled surfaces 2. Seminar on Algebraic Surfaces, University of Leiden, 8 April 2010.
Ruled surfaces 1. Seminar on Algebraic Surfaces, University of Leiden, 1 April 2010.
Parametrizations over Q of cubic surfaces. Workshop "Arithmetic aspects of elliptic surfaces", Hausdorff Institute, Bonn, 12 March 2010.
The intersection form on non-singular projective surfaces. Seminar on Algebraic Surfaces, University of Leiden, 25 February 2010.
Kwadratische reciprociteit (pdf). Bachelorseminarium, University of Leiden, 17 February 2010.
The Enriques-Kodaira classification. Seminar on Algebraic Surfaces, University of Leiden, 11 February 2010.
Reduction. Complex Multiplication Seminar, University of Leiden, 9 December 2009.
Parametrizations over Q of cubic surfaces (pdf). DIAMANT/EIDMA Symposium, Lunteren, 27 November 2009.
Class field theory. Complex Multiplication Seminar, University of Leiden, 12 November 2009.
Parametrizations over Q of cubic surfaces (pdf). About my master's thesis. Intercity Number Theory Seminar, University of Groningen, 8 May 2009.
Projectieve meetkunde en projectieve ruimten (pdf). At the "Jongerejaarscolloquium" of the FMF, University of Groningen, 4 December 2008.
De Rham-cohomologie (pdf). Studentencolloquium, University of Groningen, 18 June 2008.

Past events and courses

DIAMANT Symposium in Doorn, The Netherlands (29-30 November 2012).
Seminar on Deligne's proof of the Weil conjecture for K3 surfaces.
Seminar "Fourier analysis on number fields" (Fall 2011).
DIAMANT/EIDMA Symposium in Elspeet, The Netherlands (24-25 November 2011).
DIAMANT/EIDMA Symposium in Heeze, The Netherlands (26-27 May 2011).
Seminar on Étale Cohomology (Spring 2011).
Topics in Arithmetic Geometry 2011, Spring 2011.
Finaletraining voor deelnemers aan de Nederlandse Wiskunde Olympiade, mei-juni 2011.
Seminar on Class Field Theory (Fall 2010).
DIAMANT/EIDMA Symposium in Lunteren (25-26 November 2010).
The Arithmetic of Surfaces at the Lorentz Center. Leiden, 25-29 October 2010.
"Obstructions" seminar at Leiden University, 22-30 June 2010.
Finaletraining voor deelnemers aan de Nederlandse Wiskunde Olympiade, mei-juni 2010.
Topics in Arithmetic Geometry 2009-2010, Fall 2009-Spring 2010.
Rational Points: Theory and Experiment in Zürich, May 2010.
GTEM Workshop on Computational Number Theory and Arithmetic Geometry in Leuven, May 2010.
Seminar on Algebraic Surfaces (Spring 2010).
Seminar on Complex Multiplication (Fall 2009).
Arithmetic aspects of elliptic surfaces, workshop at the Hausdorff Institute in Bonn, 11-12 March 2010.
DIAMANT/EIDMA Symposium in Lunteren, 26-27 November 2009.

Office:	Snellius building, room 231
Postal address:	PO Box 9512, 2300 RA Leiden
Visiting address:	Niels Bohrweg 1, 2333 CA Leiden
Telephone:	071-5277131 / +31-71-5277131
E-mail:	my first name at math dot leidenuniv dot nl