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.
Geometry and Topology Seminar Speaker List
Pure Math Seminars
PDF file containing tables of generators of various cones in the Néron-Severi group of a smooth cubic surface
Publications
- Forest, Simon; Gosset, David; Kliuchnikov, Vadym; McKinnon, David, "Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets" (in submission)
- McKinnon, David; Roth, Michael, "An analogue of Liouville's Theorem and an application to cubic surfaces" (in submission).
- McKinnon, David; Roth, Michael, "Seshadri constants, Diophantine approximation, and
Roth's Theorem for arbitrary varieties", Invent. Math. 200 (2015), no. 2, 513-583
- Levin, Aaron; McKinnon, David, "Ideals of degree one contribute most of the height", Algebra Number Theory 6 (2012), no. 6, 1223--1238.
- McKinnon, David, "Vojta's Conjecture implies the Batyrev-Manin Conjecture for K3 surfaces", Bull. Lond. Math. Soc. 43 (2011), no. 6, 1111--1118.
- Logan, Adam; McKinnon, David; van Luijk, Ronald, "Density of rational points on diagonal quartic surfaces", Algebra Number Theory 4 (2010), no. 1, 1--20.
- Baragar, Arthur; McKinnon, David, "K3 surfaces, rational curves, and rational points", Journal of Number Theory 130 (2010) pp. 1470--1479
- Hare, Kevin; McKinnon, David; Sinclair, Chris, "Patterns and Periodicity in a Family of Resultants", J. Théor. Nombres Bordeaux 21 (2009), no. 1, 215--234.
- 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.
- 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.
- McKinnon, David, "Counting rational points on ruled varieties over function fields" (preprint)
- McKinnon, David, and Roth, Michael, "Curves arising from endomorphism rings of Kronecker modules", Rocky Mountain J. Math., 37 (2007), no. 3, 879-892.
- McKinnon, David, "A conjecture on rational approximations to rational points", J. Algebraic Geom., 16 (2007), 257-303.
- Magidin, Arturo, and McKinnon, David, "Gauss's Lemma for number fields", Amer. Math. Monthly 112 (2005), no. 5, 385-416.
- Etgü, Tolga; McKinnon, David; Park, B. Doug, "Lagrangian tori in homotopy elliptic surfaces", Trans. Amer. Math. Soc. 357 (2005), 3757-3774.
- McKinnon, David, "A Reduction of the Batyrev-Manin Conjecture for Kummer surfaces", Canad. Math. Bull., 47 (2004), no. 3, 398-406.
- McKinnon, David, "Counting rational points on ruled varieties", Canad. Math. Bull., 47 (2004), no. 2, 264-270.
- McKinnon, David, "Vojta's Main Conjecture for blowup surfaces", Proc. Amer. Math. Soc. 131 (2003), no. 1, 1-12.
- McKinnon, David, "An arithmetic analogue of Bezout's Theorem", Compositio. Math. 126 (2001), no. 2, 147-155.
- McKinnon, David, "Counting rational points on K3 surfaces" J. Number Theory 84 (2000), no. 1, 49-62.
Teaching (Spring 2015)
This page was last updated May 4, 2015.