Research
I work in low-dimensional topology, especially invariants of knots, surface-knots, and 3-manifolds. I am also interested in four-dimensional topology and its connections with these invariants. My research uses branched covering presentations to construct and compute 3-manifold invariants, including state-sum formulations of the Dijkgraaf–Witten invariant.
In coauthored work, I have studied 4-fold symmetric quandle invariants and their relations to Dijkgraaf–Witten and Chern–Simons invariants. My earlier work applies quandle cocycle invariants to lower bounds for the triple point numbers of surface-knots.
My recent preprint reconstructs the SU(2)-type Turaev–Viro invariant from a four-fold simple branched covering presentation.