Research

The broad domains of my research are low-dimensional topology and symplectic topology. More specifically, most of my study is into applications of Floer theory to 3-manifold topology and to knot theory. A principal subject of interest is the relationship between the symplectic and gauge-theortic types of these constructions, i.e. the various flavors of the Atiyah-Floer conjecture.

Current work

I am currently investigating the construction of a relative invariant for knots/links in 3-manifolds via traceless character varieties. This builds on the work of Henry Horton and draws additional inspiration from the formulation by Katrin Wehrheim and Chris Woodward of a Floer-theoretic invariant for tangles.