Department of Pure Mathematics University of Waterloo Waterloo, Ontario, Canada N2L 3G1 Office: MC 5167 Telephone: 519-888-4567 ext. 35560 Fax number: 519-725-0160 Email David McKinnon
David McKinnon

Research

I'm interested in arithmetic geometry, primarily the distribution of rational points on algebraic varieties, particularly surfaces. I use Vojta's Conjectures as my inspiration, so I'm always interested in special cases and consequences of them. My pet surface at the moment is a Kummer surface, but I'm not picky.

Publications

1. Logan, Adam; McKinnon, David; van Luijk, Ronald, "Density of rational points on diagonal quartic surfaces", Algebra Number Theory 4 (2010), no. 1, 1--20.
2. Baragar, Arthur; McKinnon, David, "K3 surfaces, rational curves, and rational points", to appear in J. Number Theory
3. Hare, Kevin; McKinnon, David; Sinclair, Chris, "Patterns and Periodicity in a Family of Resultants", J. Théor. Nombres Bordeaux 21 (2009), no. 1, 215--234.
4. Geelen, Jim; Guo, Anjie; McKinnon, David, "Straight line embeddings of cubic planar graphs with integer edge lengths" J. Graph Theory 58 (2008), no. 3, 270--274.
5. Levin, Aaron; McKinnon, David; Winkelmann, Jörg, "On the error terms and exceptional sets in conjectural Second Main Theorems", Q. J. Math. 59 (2008), no. 4, 487--498.
6. McKinnon, David, "Counting rational points on ruled varieties over function fields" (preprint)
7. McKinnon, David, and Roth, Michael, "Curves arising from endomorphism rings of Kronecker modules", Rocky Mountain J. Math., 37 (2007), no. 3, 879-892.
8. McKinnon, David, "A conjecture on rational approximations to rational points", J. Algebraic Geom., 16 (2007), 257-303.
9. Magidin, Arturo, and McKinnon, David, "Gauss's Lemma for number fields", Amer. Math. Monthly 112 (2005), no. 5, 385-416.
10. Etgü, Tolga; McKinnon, David; Park, B. Doug, "Lagrangian tori in homotopy elliptic surfaces", Trans. Amer. Math. Soc. 357 (2005), 3757-3774.
11. McKinnon, David, "A Reduction of the Batyrev-Manin Conjecture for Kummer surfaces", Canad. Math. Bull., 47 (2004), no. 3, 398-406.
12. McKinnon, David, "Counting rational points on ruled varieties", Canad. Math. Bull., 47 (2004), no. 2, 264-270.
13. McKinnon, David, "Vojta's Main Conjecture for blowup surfaces", Proc. Amer. Math. Soc. 131 (2003), no. 1, 1-12.
14. McKinnon, David, "An arithmetic analogue of Bezout's Theorem", Compositio. Math. 126 (2001), no. 2, 147-155.
15. McKinnon, David, "Counting rational points on K3 surfaces" J. Number Theory 84 (2000), no. 1, 49-62.

Teaching (Spring 2009)

PMATH 334 -- Introduction to Rings and Fields With Applications