Publications
. (1999). Counting rational points of bounded height on algebraic varieties. University of California, Berkeley.
. (2000). Counting rational points on K3 surfaces. Journal of Number Theory, 84, 49–62. Academic Press.
. (2001). An arithmetic analogue of Bezout's theorem. Compositio Mathematica, 126, 147–155. London Mathematical Society.
. (2003). Vojta’s main conjecture for blowup surfaces. Proceedings of the American Mathematical Society, 131, 1–12.
. (2004). A reduction of the Batyrev-Manin conjecture for Kummer surfaces. Canadian Mathematical Bulletin, 47, 398–406. Cambridge University Press.
. (2004). Counting rational points on ruled varieties. Canadian Mathematical Bulletin, 47, 264–270. Cambridge University Press.
. (2005). Gauss's lemma for number fields. The American Mathematical Monthly, 112, 385–416. Taylor & Francis.
. (2005). Lagrangian tori in homotopy elliptic surfaces. Transactions of the American Mathematical Society, 357, 3757–3774.
. (2007). A conjecture on rational approximations to rational points. Journal of Algebraic Geometry, 16, 257-303.
. (2007). Curves arising from endomorphism rings of Kronecker modules. The Rocky Mountain Journal of Mathematics, 879–892. The Rocky Mountain Mathematics Consortium.
. (2008). On the error terms and exceptional sets in conjectural second main theorems. The Quarterly Journal of Mathematics, 59, 487–498. Oxford University Press.
. (2008). Straight line embeddings of cubic planar graphs with integer edge lengths. Journal of Graph Theory, 58, 270–274. Wiley Subscription Services, Inc., A Wiley Company Hoboken.
. (2009). Patterns and periodicity in a family of resultants. Journal de théorie des nombres de Bordeaux, 21, 215–234.
. (2010). Density of rational points on diagonal quartic surfaces. Algebra & Number Theory, 4, 1–20. Mathematical Sciences Publishers.
. (2010). K3 surfaces, rational curves, and rational points. Journal of Number Theory, 130, 1470–1479. Academic Press.
. (2011). Vojta's conjecture implies the Batyrev–Manin conjecture for K 3 surfaces. Bulletin of the London Mathematical Society, 43, 1111–1118. Oxford University Press.
. (2012). Ideals of degree one contribute most of the height. Algebra & Number Theory, 6, 1223–1238. Mathematical Sciences Publishers.
. (2015). Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets. Journal of Mathematical Physics, 56. AIP Publishing.
. (2015). Seshadri constants, diophantine approximation, and Roth’s theorem for arbitrary varieties. Inventiones mathematicae, 200, 513–583. Springer Berlin Heidelberg.
