Number Theory, Diophantine Analysis, Geometry of Numbers.
My research is funded by the National Science Foundation grant DMS-1601837.
Some of my papers are available on
the arXiv .
Preprints and Publications in Refereed Journals
- (with Kevser Aktas, Kirsti Biggs, Alia Hamieh, Kathleen Petersen and Lola Thompson) Lower Bounds for Heights in Relative Galois Extensions, submitted for publication in 2017. arXiv preprint
- (with Manjul Bhargava) A positive proportion of locally soluble Thue equations are globally insoluble (preprint, 23 pages), submitted for publication in 2016. arXiv preprint
- (with N. Saradha and D. Sharma) Thue's inequalities and the hypergeometric method, to appear in the Ramanujan Journal (2017) 45 pages. arXiv preprint
- (with Jeffrey Vaaler) Minkowski's theorem on independent conjugate units the European Journal of Mathematics, 3(1), 111-149 (2017). arXiv preprint
- (with Jeffrey Vaaler) Heights, Regulators and Schinzel's determinant inequality. Acta Arithmetica 172 (2016), 285-298. arXiv preprint
- Representation of small integers by binary forms. The Quarterly Journal of Mathematics: Oxford Journals. (2015) 66 (4): 1009-1054. arXiv preprint
- Integral points on a certain family of elliptic curves. Journal de Theorie des Nombres de Bordeaux. 27 no. 2 (2015), p. 353-373. arXiv preprint
- Cubic Thue inequalities with positive discriminant. Publicationes Mathematicae Debrecen. 83/4 (2013), 727-739. arXiv preprint
(with Chantal David, Heekyoung Hahn and Lola Thompson) Distribution of squarefree values of sequences associated with elliptic curves. Contemporary Mathematics, Amer. Math. Soc. Volume 606 (2013), 171-188. arXiv preprint
- Representation of unity by binary forms. Transactions of the American Mathematical Society. 364 (2012), 2129-2155. arXiv preprint
- Upper bounds for the number of solutions to quartic Thue equations.
International Journal of Number Theory. Volume 8, Issue 2 (2012), 335-360. arXiv preprint
(With N. Saradha) Irreducibility of some orthogonal polynomials. Indagationes Mathematicae. 21 (2011), 127-137. pdf
- The method of Thue-Siegel for quartic forms. Acta Arithmetica. 141 (2010), no. 1, 1-31. arXiv preprint
- (With Ryotaro Okazaki) Quartic Thue equations. Journal of Number Theory. 130 (2010) no. 1, 40-60.
- The Diophantine equation aX^4 - bY^2 = 1. Journal fuer die reine und angewandte Mathematik (Crelle's Journal). 630 (2009), 33-57. arXiv preprint
- Cubic Thue Equations. Publicationes Mathematicae Debrecen. 75 (2009), no. 3-4, 459-483. arXiv preprint
- (with Alain Togbe and Gary Walsh) On the equation aX^4 - bY^2 = 2. Acta Arithmetica 131 (2008), 145-169.
Addendum: Acta Arithmetica 137 (2009), 199-202.
- (with Stephen Choi) On the cyclotomic Littlewood polynomials. Journal of Number Theory 128 (2008), no. 4, 884-894. pdf
- Ph.D Thesis: Thue Equations and Related Topics, University of British Columbia, 2008.
M.Sc Thesis: Characterizing Cyclotomic Littlewood Polynomials, Simon Fraser University, 2004.
Recent and Upcoming Trips