Ronald M. van Luijk

Books

• Notes on Linear Algebra 1 (based on notes by Michael Stoll).
• Notes on Linear Algebra 2 (based on notes by Michael Stoll).
• Geometry and Arithmetic of surfaces (draft version of some chapters).

Papers

• On the Galois-invariant part of the Weyl group of the Picard lattice of a K3 surface,
  to appear in Indagationes Mathematica (2024), arXiv:2304.14686 (joint with Wim Nijgh).
• Concurrent lines on del Pezzo surfaces of degree one,
  Mathematics of Computation, Volume 92 (2023), 451-481 (joint with R. Winter).
• The action of the Weyl group on the E₈ root system, and a supporting magma file,
  Graphs and Combinatorics (2021), 100pp, doi (joint with R. Winter).
• Finiteness theorems for K3 surfaces over arbitrary fields,
  European Journal of Mathematics, Volume 6 (2020), 336-366, arXiv:1810.04905 (joint with A. Logan and M. Bright).
• Unirationality of del Pezzo surfaces of degree two over finite fields,
  Bulletin of London mathematical society, volume 48, no.1 (2016), 135-140, and the extended version (joint with D. Festi).
• Computing Néron-Severi groups and cycle class groups,
  Compositio Mathematica, Volume 151 (2015), issue 04, 713-734 (joint with B. Poonen and D. Testa).
• Density of rational points on del Pezzo surfaces of degree one and accompanying files,
  Advances in Mathematics, Volume 261 (2014), 154-199 (joint with C. Salgado).
• Explicit Selmer groups for cyclic covers of P¹,
  Acta Arithmetica, Volume 159 (2013), 133-148 (joint with M. Stoll, previously titled `Unfaking the fake Selmer group').
• The Cayley-Oguiso automorphism of positive entropy on a K3 surface and other other versions and accompanying files,
  Journal of Modern Dynamics, Volume 7, No. 1 (2013), 75-97 (joint with D. Festi, A. Garbagnati, and B. van Geemen).
• Squares from blocks of consecutive integers : a problem of Erdos and Graham,
  Indagationes Math. 23 (2012), 123-127 (joint with M.A. Bennett).
• Density of rational points on elliptic surfaces,
  Acta Arithmetica, Volume 156, no. 2 (2012), 189-199.
• Two-coverings of Jacobians of curves of genus two,
  Proc. London Math. Soc. (3) 104 (2012), 387-429 (joint with E.V. Flynn and D. Testa).
• On character varieties of two-bridge knot groups,
  Proc. London Math. Soc. (2) 103 (2011), 473-507 (joint with M. Macasieb and K. Petersen).
• Cubics points on cubic curves and the Brauer-Manin obstruction for K3 surfaces,
  Acta Arithmetica, Volume 146, no. 2 (2011), 153-172, and accompanying files, also available at arXiv:0708.2752.
• Wehler K3 surfaces with Picard number 3 and 4. Appendix to: Orbits of points on certain K3 surfaces, by Arthur Baragar,
  Journal of Number Theory, Volume 131, Issue 3 (2011), 600-603.
• Density of rational points on diagonal quartic surfaces,
  Algebra and Number Theory, Vol. 4, No. 1 (2010), 1-20 (joint with A. Logan and D. McKinnon).
• Lines on Fermat surfaces,
  Journal of Number Theory, Volume 130, Issue 9 (2010), 1939-1963, and accompanying files, also available at arXiv:0812.2377 (joint with M. Schütt and T. Shioda)
• Nontrivial elements of Sha explained through K3 surfaces and accompanying files,
  Math. Comp. 78 (2009), 441-483. (joint work with Adam Logan, also available at arXiv:0706.0541).
• Non-Euclidean Pythagorean triples, a problem of Euler, and rational points on K3 surfaces,
  Mathematical Intelligencer, Vol. 30, No. 4 (2008), 4-10 (joint work with Robin Hartshorne, also vailable at arXiv:math.NT/0606700).
• The diameter of the circumcircle of a Heron triangle,
  Elemente der Mathematik, Vol. 63, Issue 3 (2008), p. 118-121.
• K3 surfaces with Picard number one and infinitely many rational points,
  Algebra and Number Theory, Vol. 1, No. 1 (2007), 1-15.
• K3 surfaces with Picard number three and canonical vector heights,
  Mathematics of Computation, Volume 76 (2007), 1493-1498 (joint work with Arthur Baragar, different version available at arXiv:math.AG/0602166 ).
• An elliptic K3 surface associated to Heron triangles,
  Journal of Number Theory, Volume 123 (2007), 92-119, also available at arXiv:math.AG/0411606 (erratum).
• A K3 surface associated to certain integral matrices with integral eigenvalues,
  Canadian Mathematical Bulletin, Volume 49 (4), 2006, 560-577, also available at arXiv:math.AG/0411600.
• Quartic K3 surfaces without nontrivial automorphisms,
  Mathematical Research Letters (MRL), Volume 13 (2006), Issue 3, 423-439, also available at arXiv:math.AG/0511542.
• A linear algebra exercise,
  Nieuw Archief voor Wiskunde (NAW), Juni 2002, 139-140 (joint with F. Beukers and R. Vidunas).

Theses

• On perfect Cuboids, my undergraduate thesis.
• Rational points on K3 surfaces, my graduate thesis.

Various

• NMC nieuwe stijl, Nieuw Archief voor Wiskunde, June 2015, 130-132 (Dutch).
• 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.