I am an Assistant Professor of mathematics at Oklahoma State University. In Fall 2011, I will be teaching two sections of of Multi-variable Calculus. My research focusses on surfaces in 3-dimensional manifolds, with a particular focus on Heegaard splittings. A Heegaard splitting is a decomposition of a 3-manifold into an orientable surface and a pair of handlebodies such that the interiors of the handlebodies form the complement of the surface. Heegaard splittings are often used as a tool to prove other things about 3-manifolds, but they are also worth studying in and of themselves. My research is partially funded by an NSF Grant (DMS-1006369) titled "The Geometry and Topology of Heegaard Splittings."

If you'd like to know more about Heegaard splittings, a good place to start is the survey paper written by Martin Scharlemann. This gives a nice overview of the subject, as it stood a few years ago: what was known, open problems, useful tools and sketches of important proofs.

I've written some notes, which consist of five chapters, beginning with the basic definitions of handlebodies and Heegaard splittings and concluding with proofs Waldhausen's Theorem, the Reidemeister-Singer Theorem and Casson and Gordon's famous result weakly reducible splittings and incompressible surfaces. These cover less material that Scharlemann's survey, but with more details. If you happen to look at them, I would be very interested in any feedback you can give me.

I have a blog with Nathan Dunfield, Henry Wilton and Daniel Moskovich covering current research in low dimensional topology, and most of my posts are related to Heegaard splittings and their close relations.

The papers I've written can all be found on the ArXiv. But for an organized list, you can read my annotated bibliography.