Publications
An analogue of Liouville’s theorem and an application to cubic surfaces. European Journal of Mathematics, 2, 929–959. Springer International Publishing Cham.
. (2016). Approximating rational points on surfaces. arXiv preprint arXiv:2403.02480. Retrieved from http://arxiv.org/abs/2403.02480
. (2024). Approximating rational points on toric varieties. Transactions of the American Mathematical Society, 374, 3557–3577.
. (2021). An arithmetic analogue of Bezout's theorem. Compositio Mathematica, 126, 147–155. London Mathematical Society.
. (2001). The arithmetic puncturing problem and integral points. arXiv preprint arXiv:1806.03180.
. (2018). Codimension two integral points on some rationally connected threefolds are potentially dense. J. Algebraic Geometry, 31, 345-386.
. (2022). A conjecture on rational approximations to rational points. Journal of Algebraic Geometry, 16, 257-303.
. (2007). Counting rational points of bounded height on algebraic varieties. University of California, Berkeley.
. (1999). . (2000). Counting rational points on ruled varieties. Canadian Mathematical Bulletin, 47, 264–270. Cambridge University Press.
. (2004). . (2019). Curves arising from endomorphism rings of Kronecker modules. The Rocky Mountain Journal of Mathematics, 879–892. The Rocky Mountain Mathematics Consortium.
. (2007). On curves with high multiplicity on P (a, b, c) for min (a, b, c). NEW YORK JOURNAL OF MATHEMATICS, 27, 1060–1084. ELECTRONIC JOURNALS PROJECT UNIV ALBANY, DEPT MATHEMATICS & SCIENCE, ALBANY ….
. (2021). Density of rational points on diagonal quartic surfaces. Algebra & Number Theory, 4, 1–20. Mathematical Sciences Publishers.
. (2010). . (2023).
On the error terms and exceptional sets in conjectural second main theorems. The Quarterly Journal of Mathematics, 59, 487–498. Oxford University Press.
. (2008). Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets. Journal of Mathematical Physics, 56. AIP Publishing.
. (2015). . (2005).
Ideals of degree one contribute most of the height. Algebra & Number Theory, 6, 1223–1238. Mathematical Sciences Publishers.
. (2012). K3 surfaces, rational curves, and rational points. Journal of Number Theory, 130, 1470–1479. Academic Press.
. (2010).