My work as a mathematician lies at the intersection of topology, combinatorics, and computer science. In my thesis, I worked with triangualtions of surfaces, arc complexes, and branched covering maps. I created an algorithm for deciding when a triangulation of a surface can be made by lifting (informally, a sort of unfolding) a triangulation of a punctured disk under a branched covering map. If you're interested in learning more, check out my paper on the arXiv.
Understanding the shape of the set of triangulations which can be made this way motivated that work. My current work in pure math is on a conjecture about this strange space. If you'd like to know more about the conjecture and how it fits in with an invariant of 3-dimensional manifolds called Heegaard-Floer homology, you'll find it in my research statement.