Generally I work in the field of low dimensional topology. I am interested in knot theory, braid groups, and other visual/combinatorial objects. I like to study maps between things, so I am naturally drawn to combinatorial representation theory, finite type invariants, planar algebras, and quantum computing.
The topic of my thesis was finding discrete representations of the braid groups into lattices. My approach was to specialize the parameter of the representation to certain Salem numbers, and harness the algebraic properties of the Salem numbers to guarantee discreteness of the representation.
Since graduating, I have focused my research towards virtual knot theory and more general studies of the braid groups.
Here is my CV.
Here are my papers:
An Invariant of Virtual Trivalent Spatial Graphs, joint with Sherilyn Tamagawa
Finite Image Homomorphisms of the Braid Group and its Generalizations Joint with Yvon Veberne
OC relation— A quick proof of a known fact that the OC relation can be written in two ways.
Ribbon 2-Knots, 1+1=2, and Duflo’s Theorem for Arbitrary Lie Algebras joint with Dror Bar-Natan and Zsuzsanna Dancso