#### Research Interest

I mostly like to think about knots in 3-manifolds.
Currently, I'm trying to understand when the fundamental group of the complement of a knot in S^{3} is bi-orderable,
i.e. has a total order invariant under both left and right multiplication.
Some examples of knots with bi-orderable knot groups are the figure 8 knot, the stevedore knot, and the pretzel knot P(-3,3,3).
Typically, knot groups are not bi-orderable
so naturally one wonders, "When a knot does have a bi-orderable knot group what does this tell us about the topology of the knot?"
This is the motivating question behind my research.

#### Publications and Works in Progress

♦ Residual torsion-free nilpotence, bi-orderability, and two-bridge links, *Canadian Journal of Mathematics* (2023)

♦ Residual torsion-free nilpotence, bi-orderability and pretzel knots, *Algebraic and Geometric Topology* 24, 4 (2023)

♦ Non-standard bi-orders on punctured torus bundles, preprint, w/ H. Segerman

♦ Algorithmic obstructions and order-preserving braids, preprint, w/ N. Scherich and H. Turner

♦ Bi-orderability and double twist links, in preparation