Research

While at Georgia Tech, I completed four semesters of undergraduate research: two as part of Georgia Tech’s REU program, and two for my senior project.

Summer 2010 REU

In the Summer of 2010 I worked with David Lowry under the direction of Ernie Croot on the Polymath4 Project, the goal of which was to develop a fast (better than O(10^√n)) algorithm for locating large prime numbers. We attacked a number of different angles, but most of our time was spent trying to find a (Strassen variant) algorithm for multiplying matrices of a particular form or to find an algorithm for evaluating sparse, high-degree polynomials.

Summer 2011 REU

In the Summer of 2011 I worked under the direction of H. Venkateswaran and Prasad Tetali on a project in complexity theory. The overarching goal was to describe naturally a class C of computational problems such that the Bipartite Perfect Matching problem is complete for C. Our approach centered on trying to find a class of boolean cicuits which could be converted in logspace into flow networks with capacities in unary (using a construction like in Goldschlager, et al 1982).

I presented a poster on this project at the School of Math alumni gathering

Senior Project

In the Fall and Spring of 2011 I worked on different aspects of a project under the direction of Douglas Ulmer. The overarching goal was to enumerate the generators of a particular elliptic curve group over F_p(x). The first semester was focused on algebraic techniques, looking at different actions on known generators. The second was focused on combinatorial techniques, trying to discern the structure of the quotient of our group with the subgroup generated by the known generators.