My research focuses on knots and three-manifolds. I am particularly interested in the Floer-theoretic tools of Heegaard Floer theory and contact homology. Both of these are defined via pseudoholomorphic curves in symplectic manifolds, but they can also be approached from a combinatorial perspective as well. Generally speaking, the geometric theories are more powerful while the combinatorial versions are easier to work with. I study the interplay between these two viewpoints as well as their applications to topological and contact geometric questions. In addition to contact geometry, I am also interested in topological topics such as Dehn surgery, Heegaard splittings, and link genus.
Papers
Legendrian grid number one knots and augmentations of their differential algebras, submitted.