Research

Research Statement

This document contains a summary of the mathematics research I produced while in grad school, and some ideas for future research directions. There is also a description of my plans for a surface visualization program.
Get the pdf here.

Graduate Research Articles

Calculating the homology and intersection form of a 4-manifold from a trisection diagram. (2017)
With Peter Feller, Michael Klug, and Trent Schirmer.
Submitted for publication. (arXiv link)
The simple loop conjecture for 3-manifolds modeled on Sol. (2016)
Published in Algebraic & Geometric Topology, 2016. (journal link) (arXiv link)

Undergraduate Research Articles

Unary pattern avoidance in partial words dense with holes. (2011)
With Francine Blanchet-Sadri and Kevin Black.
Published in Language and Automata Theory and Applications. (journal link)
Greedy algorithms for generalized k-rankings of paths. (2010)
With Sandra James and Darren A. Narayan.
Published in Information Processing Letters. (journal link)
Minimal k-rankings for prism graphs. (2010)
With Juan Ortiz, Hala King, Darren A. Narayan, and Mirko Hornak.
Published in Involve. (journal link)