Research
Soap Bubbles and Films
I did undergraduate research with Gary Lawlor about minimal surfaces. My original paper was not published, but I think the computations there were very interesting, so I'm making it available here.I am a coauthor of a paper that contains a generalization of this result: Rebecca Dorff, Drew Johnson, Gary R. Lawlor, Donald Sampson. Isoperimetric surfaces with boundary. Proc. Amer. Math. Soc. 139 (2011), pp. 4467-4473.
IMPACT
I also participated in the IMPACT undergraduate reseach program at BYU, headed by Jeff Humperys. My project involoved working with Dennis Tolley on analyzing GC/MS data. My write up is available here. I learned MATLAB while in this program.
FJRW Theory
As a masters student, my advisor was Tyler Jarvis. I worked with FJRW theory, and my thesis was proving a new result in Landau-Ginzburg mirror symmetry. I also implemented Sage code to compute invariants in the FJRW theory. A small generalization of my thesis has been condensed and submitted to the String-Math 2011 conference proceedings and is available on the arXiv .
Intersections on Moduli of Curves
I also wrote code in Sage for computing top intersections on the moduli space of curves. (Click here for a demo printed from a sage notebook, or here for the source code.)
Tropical Geomtry
I am currently working with Aaron Bertram and learning some Tropical geometry. Hopefully soon there will be some cool results to post here.