•Research•

My research interests are in Number Theory, with a focus on the arithmetic theory of quadratic forms. I am particularly interested in applying the techniques developed for integral quadratic forms to study the representations of inhomogeneous quadratic forms. Here is a link to my curriculum vitae. My thesis advisor is Wai Kiu Chan.

Publications

1. On almost universal ternary inhomogeneous quadratic polynomials, (Thesis, in progress).
2. Almost Universal Ternary Sums of Squares and Triangular Numbers, (To appear in "Quadratic and Higher Degree Forms," Developments in Mathematics, Springer-Verlag).
3. Primitive Prime Divisors in Zero Orbits of Polynomials, INTEGERS, Vol. 12 (2012).

Sage

Sage is an open-source math software (an alternative to Mathematica) which supports computation in Number Theory. I'm a member of the Sage community, and am interested in developing Sage, in particular its applications to Quadratic Forms. Here are some useful links for downloading, using, and developing Sage.

Below is a program that I wrote for sage. It implements the algorithm for deciding almost universality, as described in my thesis. Given a quadratic Lattice $N$, this program returns a list of suitable vectors $v$, for which the inhomogeneous polynomial $v+N$ is almost universal. The following patch can be applied to Sage 4.7.1. Currently the program is only equipped to handle a certain class of lattices, namely those which are ternary, positive definite, and anisotropic at a single odd prime.

•Home•