I received my PhD from the Massachusetts Institute of Technology (MIT). I am currently a Queen’s Research Chair in Mathematics, with a cross-appointment to Philosophy. I have been the winner of the Queen’s Research Prize, and the Coxeter-James Prize and many other honours in mathematics, and am a Fellow of the Royal Society of Canada. In Philosophy my interests relate to Indian philosophy and in mathematical logic.
Specialising in number theory, I focus my research in the areas of modular forms, elliptic curves, and sieve theory.
- The Art of Research, 2005 Herzberg Lecture, Carleton University/Tata Institute for Fundamental Research, Mumbai, India.
- Ellipses and elliptic curves, Coleman-Ellis Lecture, March 30, 2006.
- Recent Developments in the Langlands Program, C.R. Math. Acad. Sci. R. Can., 24(2002), no. 2, 33-54.
- A Motivated Introduction to the Langlands Program, in Advances in Number Theory, (edited by F. Gouvea and N. Yui), pp. 37-66, Clarendon Press, Oxford, 1993.
- Ramanujan graphs, Journal of the Ramanujan Math. Society, 18, No. 1, (2003), 1-20.
- Selberg’s conjectures and Artin L-functions, Bulletin of the American Math. Society, 31(1) (1994), 1-14.
- Sudoku squares and chromatic polynomials(with A. Herzberg), Notices of the Amer. Math. Society, 54(2007), no. 6, 708-717.
- Multiple Hurwitz zeta functions (with K. Sinha), in Multiple Dirichlet series, automorphic forms, and analytic number theory, Proc. Symp. Pure Math., 75 (2006), 135-156.
- An introduction to sieve methods and their applications, (with A. Cojocaru) London Mathematical Society Student Texts, 66, Cambridge University Press, 2006.
- Problems in Algebraic Number Theory, (with J. Esmonde), Graduate Texts in Mathematics, 190, Springer-Verlag, 2005, 2nd edition.