Ronald M. van Luijk

Papers

• Quartic K3 surfaces without nontrivial automorphisms and in PDF, Mathematical Research Letters (MRL), Volume 13 (2006), Issue 3, 423-439, also available at arXiv:math.AG/0511542).
• A linear algebra exercise, with F. Beukers and R. Vidunas, Nieuw Archief voor Wiskunde (NAW), Juni 2002, 139-140.
• On perfect Cuboids, my undergraduate thesis.

• A K3 surface associated to certain integral matrices with integral eigenvalues and in PDF (accepted by the Canadian Mathematical Bulletin, also available at arXiv:math.AG/0411600).
• An elliptic K3 surface associated to Heron triangles and in PDF (accepted by Journal of Number Theory, also available at arXiv:math.AG/0411606).
• K3 surfaces with Picard number three and canonical vector heights and in PDF (joint work with Arthur Baragar, different version available at arXiv:math.AG/0602166 ).

• K3 surfaces with Picard number one and infinitely many rational points and in PDF (also available at arXiv:math.AG/0506416).
• The diameter of the circumcircle of a Heron triangle and in PDF
• Non-Euclidean Pythagorean triples, a problem of Euler, and rational points on K3 surfaces and in PDF (joint work with Robin Hartshorne, also vailable at arXiv:math.NT/0606700).

• Toward an explicit 2-descent on the Jacobian of a generic curve of genus 2 (joint work with Adam Logan).

Slides

• An elliptic K3 surface associated to Heron triangles (Colloquium talk at Queen's University)
• K3 surfaces with Picard number one and infinitely many rational points (number theory seminar at Queen's University)
• Explicit computations on the Manin conjectures (workshop "Explicit methods in number theory" at Oberwolfach)
• Toward an explicit 2-descent on the Jacobian of a generic curve of genus 2 (AMS meeting San Antonio, Jan. 2006)
• Nontrivial Sha for curves of genus 2 arising from K3 surfaces (UC San Diego, May 2006)
• Manin conjectures for K3 surfaces (Banff, Canada, May 2006)
• Introduction Number Theory in Cryptography (Bogota, Colombia, September 2006)

Pictures

• A K3 surface with infinitely many rational points (The cover of my thesis)

Various

• Wiskunde Olympiade with Jan van de Craats and Thijs Notenboom, Nieuw Archief voor Wiskunde, December 2000, 448-450 (Dutch).
• Hex, dots and boxes with Sander van Rijnswou, Nieuw Archief voor Wiskunde, December 2001, 358-361 (Dutch).
• IMO95 puzzles, Crux Mathematicorum, No. 2, Vol. 22, March 1996, 70.