Research
My area of research is lowdimensional topology. I am interested in Khovanov homology and Heegaard Floer homology, and my work is informed by connections between these two theories. To date, this has fallen along two distinct but, as it happens, quite interconnected lines of inquiry:
Symmetries and Khovanov homology
The relationship between Khovanov homology and Heegaard Floer homology by way of double branched covers suggests where to look for new applications in Khovanov homology. This seems to strengthen the connection between the two theories and gives rise, for example, to an algebraic tool for studying the mapping class group of the knot complement (also known as the knot's symmetry group).
Lspaces and leftorderability
The simplest threemanifolds, from the vantage point of Heegaard Floer theory, are Lspaces. These come up in application and satisfy interesting properties, but a complete understanding of Lspaces is lacking. However, there appear to be strong connections with foliations and leftorderable groups.
Publications
My papers on the arXiv,
MathSciNet,
zbMATH and
Enlighten.
These are listed below in (approximate) reverse chronological order.
Preprints and works in preparation

Bordered Floer homology for manifolds with torus boundary via immersed curves
(with Jonathan Hanselman and Jake Rasmussen)
Submitted, arXiv.1604.03466.

Taut foliations on graph manifolds
(with Jonathan Hanselman, Jake Rasmussen and Sarah Rasmussen)
Submitted, arXiv.1508.05911.

A calculus for bordered Floer homology (with Jonathan Hanselman)
Submitted, arXiv.1508.05445.
Slides from the EMS/SCM Joint Meetings (2015)

Khovanov homology and the symmetry group of a knot
Submitted, arXiv.1311.1085.
Accompanying Mathematica notebook for some of the calculations for this paper using KnotTheory`.

Heegaard Floer homology solid tori
In preparation.
Videos of talks on this material from BIRS
and from SCGP.
Slides from the AMS Joint Meetings (2013) and from the CMS Winter Meeting (2013).

On the geography and botany of knot Floer homology
(with Matt Hedden)
Submitted, arXiv:1404.6913.
Published, in press, or accepted

The Alexander invariant, Seifert forms, and categorification
(with Jen Hom and Tye Lidman)
To appear in Journal of Topology, arXiv:1501.04866.

Nonfibered Lspace knots
(with Tye Lidman)
Pacific Journal of Mathematics, Volume 267, Number 2 (2014).
 Genus one open books with nonleftorderable fundamental group
(with Yu Li)
Proceedings of the American Mathematical Society, Volume 142 Number 4 (2014).

Graph manifolds, leftorderability and amalgamation
(with Adam Clay and Tye Lidman)
Algebraic and Geometric Topology, Volume 13, Number 4 (2013).

On Lspaces and leftorderable fundamental groups
(with Steve Boyer and Cameron Gordon)
Mathematische Annalen, Volume 356, Issue 4 (2013).
 New proofs of certain finite filling results via Khovanov homology
Quantum Topology, Volume 4 Number 4 (2013).
 Turaev torsion, definite 4manifolds and quasialternating knots
(with Josh Greene)
Bulletin of the London Mathematical Society, Volume 45 Number 5 (2013).
 Leftorderable fundamental groups and Dehn surgery
(with Adam Clay)
International Mathematics Research Notices, Number 12 (2013).
 Surgery obstructions from Khovanov homology
Selecta Mathematica Volume 18 Number 2 (2012).
Slides from my talk at the Georgia Topology Conference.
 On cabled knots, Dehn surgery, and leftorderable fundamental groups
(with Adam Clay)
Mathematical Research Letters, Volume 18 Number 6 (2011)
 A surgical perspective on quasialternating links
Lowdimensional and Symplectic Topology, Volume 82 of Proceedings of Symposia in Pure Mathematics (2011)
 Does Khovanov homology detect the unknot?
(with Matt Hedden)
American Journal of Mathematics, Volume 132 Number 5 (2010).
 A remark on Khovanov homology and twofold branched covers
Pacific Journal of Mathematics, Volume 245 Number 2 (2010).
Accompanying Mathematica notebook performing the calculations in this paper using KnotTheory`.
 Knots with identical Khovanov homology
Algebraic and Geometric Topology, Volume 7 (2007).
 Simplification of scalar data via monotonelight factorizations (with Martin Brooks)
Proceedings of the 19th Canadian Conference on Computational Geometry, (2007).
 Any tangle extends to nonmutant knots with the same Jones polynomial
Journal of Knot Theory and its Ramifications, Volume 15 Number 9 (2006).
Theses
 Involutions on 3manifolds and Khovanov homology
UQÀM
PhD thesis (June 2009)
Supervisor: Steve Boyer
 Knots, tangles and braid actions
UBC
MSc thesis (October 2004)
Supervisor: Dale Rolfsen
Other writing
 Simplification of sampled scalar fields by removal of extrema
(with Martin Brooks)
NRC Technical Report (2007).