My research interests are primarily in Newton polygons of L-Functions of exponential sums, primarily motivated by the tools developed by Daqing Wan. I hope to use these tools to investigate asymptotic variation of these polygons as p tends toward infinity. Lower bounds are well established. Asymptotic behavior us understood in one dimension and a few cases of two but higher analogues remain.
I also use some exponential sum methods in algebraic trace codes. Some of my work is trying to extend results of Marcel Van Der Vlugt. I am currently investigating the computational limits of these results.
Regular decomposition of ordinarity in generic exponential sums
I gave this talk in the "Expository talks for Undergraduates by Graduate Students" at Mathfest in 2009. As the name suggests this talk is geared toward undergraduate mathematics students.
This is a talk on current research on Algebro Geometric Trace codes that I presented at the 2012 Joint Mathematics Meeting.
These are the slides I presented in defense of my dissertation in 2009 at UCI.