My research lies at the interface of geometric topology and higher category theory, with a focus on low-dimensional topological quantum field theory (TQFT). I am particularly interested in explicit generators-and-relations presentations of bordism bicategories and their applications to the construction and classification of (partially defined) 3-dimensional TQFTs. I am also increasingly interested in link homology theories and (associated) 4-dimensional TQFTs.
Theses
On surgery presentations of bordism bicategories. Advisors: Christopher Douglas and Bruce Bartlett. Doctoral thesis, available here.
On Kontsevich's characteristic classes. Advisor: Peter Kronheimer. Undergraduate thesis, available upon request.