Geometry, topology, algebra, and mathematical physics; particularly, their interaction. (I may make this more precise at some point.)
Writings
This is a selection of my mathematical writings. Some are rough and/or unfinished, and such cases are noted. Also see the group math blog Concrete Nonsense, of which I am one of three founders.
Notes on the X-ray Transform in Geometry and Dynamics (Mar. 2008): My notes on Gabriel Paternain's course, "The X-ray Transform in Geometry and Dynamics", a Part III course at Cambridge from the Lent term of 2008. (Updated June 2008.)
Spin Geometry on Surfaces (Apr. 2007): My Harvard undergraduate thesis (advisor: Clifford Taubes). Spin and spin-c structures, as well as complex spinor bundles, are constructed and studied, with particular attention paid to the case of closed orientable (real) surfaces.
Dunking Donuts: Culinary Calculations of the Euler Characteristic (Dec. 2006): A slightly expanded, written version of a talk I gave at the Harvard Math Table (undergraduate colloquium) on November 28, 2006. Morse theory and the Poincaré-Hopf Index Theorem are introduced as ways to calculate the Euler characteristic. The title refers to two culinary analogies used in the case of closed surfaces. Published in the Harvard College Mathematics Review (Vol. 1, No. 1, Spring 2007).
Notes on Topological Tic-Tac-Toe (Oct. 2006): A section handout I wrote as the course assistant for Harvard Math 131, Topology (taught by Véronique Godin). Tic-tac-toe is considered on the torus, the projective plane, the Klein bottle, the cylinder, and the Möbius strip. This is very sparse, closer to an outline than actual notes. A much more complete exposition I have written can be fond at Concrete Nonsense (direct links: 1, 2).