Ronald M. van Luijk
- Finiteness theorems for K3 surfaces over arbitrary fields, to be published in European Journal of Mathematics, 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 and in PDF, 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 and in PDF, Elemente der Mathematik, Vol. 63, Issue 3 (2008), p. 118-121.
- K3 surfaces with Picard number one and infinitely many rational points and in PDF, Algebra and Number Theory,
Vol. 1, No. 1 (2007), 1-15.
- K3 surfaces with Picard number
three and canonical vector heights
and in PDF, 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 and in
PDF, Journal of Number Theory, Volume 123 (2007), 92-119, also available at
- A K3 surface
associated to certain integral matrices with integral
eigenvalues and in PDF
Canadian Mathematical Bulletin,
Volume 49 (4), 2006, 560-577, also available at
- Quartic K3 surfaces without nontrivial automorphisms and in
PDF, Mathematical Research Letters (MRL), Volume 13 (2006), Issue 3, 423-439, also available at
linear algebra exercise, with F. Beukers and R. Vidunas, Nieuw
Archief voor Wiskunde (NAW), Juni 2002, 139-140.
The slides I used for some presentations:
- Density of rational points on Del Pezzo surfaces of degree one and the video at BIRS (Oaxaca, 2018)
- Arithmetic of K3 surfaces (open problems and conjectures) (Leiden, 2015)
- Concurrent lines on del Pezzo surfaces of degree one and the talk on youtube (Rio de Janeiro, 2015)
- Geometry dictates arithmetic (Utrecht, 2013)
- Computing Néron-Severi groups (AIM, Palo Alto, 2013)
- De kunst en het nut van factoriseren (Nationale Wiskunde Dagen, 2013)
- Density of rational points on Del Pezzo surfaces of degree one (Lausanne, Switzerland, 2012)
- Computing Picard groups of surfaces (Tokyo, February 2010)
- Cubic points on cubic curves and the Brauer-Manin obstruction on K3 surfaces (Bristol, UK, July 2007)
- Introduction Number Theory in Cryptography (Bogota, Colombia, September 2006)
- Manin conjectures for K3 surfaces (Banff, Canada, May 2006)
- Nontrivial Sha for curves of genus 2 arising from K3 surfaces (UC San Diego, May 2006)
- Toward an explicit 2-descent on the Jacobian of a generic curve of genus 2 (AMS meeting San Antonio, Jan. 2006)
- Explicit computations on the Manin conjectures (workshop "Explicit methods in number theory" at Oberwolfach)
- 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)
- 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.
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