Research

 

Click here for my CV, or here to read the research statement I submitted with my job applications, or read on for a summary of some of my projects.

 

 

Strange Duality

I am currently working with Aaron Bertram on a project involving "Strange Duality" for moduli spaces of sheaves on del Pezzo surfaces. We have some interesting computations involving multiple point formulas that match with computations of Euler characteristics of theta line bundles for moduli spaces of sheaves. We hope to have a preprint ready by the end of the semester!

 

Tropical Geomtry

I did some work on Tropical Geometry. I have a result about when points in tropical affine space uniquely determine a hypersurfaces. I have given some talks about this. The paper is submitted for publication. You can find a preprint on the arXiv.

 

Intersections on Moduli of Curves

I also wrote code in Sage for computing top intersections on the moduli space of curves. (View a demo in the Sage Math Cloud. or here is the source code.)

 

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 published in Procedings of Symposia in Pure Mathematics: String-Math 2011. The full text is available on the arXiv.

 

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.

 

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.