Oklahoma State University
Department of Mathematics
|(405)744-7750||Stillwater, OK 74078|
I am an Assistant Professor of mathematics at Oklahoma State University. In Spring 2012, I am teaching Multi-variable Calculus (Math 2163) and Introduction to Modern Algebra (Math 3613).
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 have a blog with Nathan Dunfield, Henry Wilton and Daniel Moskovich covering current research in low dimensional topology. Most of my posts are related to Heegaard splittings and their close relations, though I've recently been writing a series of posts about applied topology.