Number Theory, Diophantine Analysis, Transcendence theory.
Some of my papers are available on
the arXiv .
List of Publications in Refereed Journals
- Cubic Thue inequalities with positive discriminant. Publicationes Mathematicae Debrecen. 83/4 (2013), 727-739.
(with David, C., Hahn, H. and Thompson, H.) Distribution of squarefree values of sequences associated with elliptic curves. Contemporary Mathematics, Amer. Math. Soc. Volume 606 (2013), 171-188.
- Representation of unity by binary forms. Transactions of American Mathematical Society. 364 (2012), 2129-2155.
- Upper bounds for the number of solutions to quartic Thue equations.
International Journal of Number Theory. Volume 8, Issue 2 (2012), 335-360.
(With Saradha, N.) Irreducibility of some orthogonal polynomials. Indagationes Mathematicae. 21 (2011), 127-137.
- The method of Thue-Siegel for quartic forms. Acta Arithmetica. 141 (2010), no. 1, 1-31.
- (With Okazaki, R.) 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.
- Cubic Thue Equations. Publicationes Mathematicae Debrecen. 75 (2009), no. 3-4, 459-483.
- (with Togbe, A. and Walsh, P. G.) On the equation aX^4 - bY^2 = 2. Acta Arithmetica 131 (2008), 145-169.
Addendum: Acta Arithmetica 137 (2009), 199-202.
- (with Choi, K. K.) On the cyclotomic Littlewood polynomials. Journal of Number Theory 128 (2008), no. 4, 884-894.
Works in Progress
- Representation of small integers by binary forms. (submitted)
- (with Bhargava. M.) Binary cubic forms that do not represent 1.
- Integral points on a family of elliptic curves.
- Ph.D Thesis: Thue Equations and Related Topics, University of British Columbia, 2008.
M.Sc Thesis: Characterizing Cyclotomic Littlewood Polynomials, Simon Fraser University, 2004.
- Diophantine Equations, Shimla, India, June 30-July 19, 2014.
- Workshop: Analytic Number Theory, Mathematik-Zentrum, Bonn, Germany, July 11-18, 2014.
Max Planck Institute, Bonn, Germany, August and September 2014.
- Approximation diophantienne et transcendance, CIRM, Luminy, France, September 15-September 19, 2014.
- Hausdorff Institute, Bonn, Germany, Jan-March 2013.
- AMS Western Section meeting in Boulder, 13-14 April 2013.
- University of Texas, Austin, 18 April 2013.
ARCTIC NUMBER THEORY WORKSHOP, SAARISELKÄ, LAPLAND, FINLAND, 15-20 June 2013.
- KTH, Stockholm, Sweden, June 26-June 29, 2013.
- Thue 150, Bordeaux, France, September 30-October 4, 2013. (Supported by AWM-NSF Travel Grant).
- Grenoble, Lyon and Saint-Etienne Number Theory seminar, Saint-Etienne, France, October 10, 2013.
- Programme on Heights in Diophantine geometry, group theory and additive combinatorics
a>, ESI, Vienna, Austria, Nov 2013.