Research
I study problems in lowdimensional topology, using invariants like Khovanov homology and Heegaard Floer homology.
Most recently, this has involved working with bordered Floer homology, towards understanding the link between taut foliations, leftorders, and nonLspaces.
My research is supported by a grant from the Natural Sciences and Engineering Research Council of Canada (NSERC),
and I am privileged to carry out my work on the traditional, ancestral, and unceded territory of the x^{w}mǝθk^{w}ǝy̓ǝm (Musqueam) People.
I am part of the topology group at UBC. Our seminar meets Wednesdays from 3:00 to 4:00 – currently virtually.
I am involved in the PIMS CRG Novel Techniques in Low Dimension.
My office is in Mathematics 219. The best way to contact me is by email: liam[at]math[dot]ubc[dot]ca
Instagram: @mathonmydeskrightnow
Publications
My papers on the
arXiv,
MathSciNet, and
zbMATH.
These are listed below in (approximate) reverse chronological order.
Preprints and works in preparation

Thin links and Conway spheres
(with Artem Kotelskiy and Claudius Zibrowius)
In preparation.

Khovanov homology and strong inversions
(with Artem Kotelskiy and Claudius Zibrowius)
Submitted.

A mnemonic for the Lipshitz–Ozsváth–Thurston correspondence
(with Artem Kotelskiy and Claudius Zibrowius)
Submitted arXiv.2005.02792.

Khovanov invariants via Fukaya categories: The tangle invariants agree
(with Artem Kotelskiy and Claudius Zibrowius)
Submitted arXiv.2004.01619.

Immersed curves in Khovanov homology
(with Artem Kotelskiy and Claudius Zibrowius)
Submitted arXiv.1910.14584.
Computational software associated with these invariants, due to Gurkeerat Chhina and Claudius Zibrowius, is available at GitHub.
Sample tangles and associated calculations are collected at the nascent tangle atlas, compiled by Leon Yao.

Cabling in terms of immersed curves
(with Jonathan Hanselman)
Submitted arXiv.1908.04397.

Heegaard Floer homology for manifolds with torus boundary: properties and examples
(with Jonathan Hanselman and Jake Rasmussen)
Submitted, arXiv.1810.10355.
This includes some older writing on Heegaard Floer homology solid tori which never appeared, though there are videos of talks on this material from BIRS
and from SCGP as well as slides from the AMS Joint Meetings (2013) and from the CMS Winter Meeting (2013).

Bordered Floer homology for manifolds with torus boundary via immersed curves
(with Jonathan Hanselman and Jake Rasmussen)
Submitted, arXiv.1604.03466.
Slides from the Mathematical Congress of the Americas (2017).
Videos of talks on this material from CMO (2017):
Part 1
and
Part 2.
Other talks on this material were recorded at INI (2017) as part of the program Homology theories in lowdimensions.
Videos of talks on (older versions of) this material from BIRS (2016):
Part 1.
and
Part 2

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

A refinement of Khovanov homology
(with Andrew Lobb)
To appear in Geometry & Topology, arXiv.1908.00082.
Some additional comments on separating mutants, which simplify/clarify/generalize a construction in this paper, can be found here.
These will be incorporated into the published version of the paper; here is an up to date version of the paper.

Lspaces, taut foliations, and graph manifolds
(with Jonathan Hanselman, Jake Rasmussen and Sarah Rasmussen)
Compositio Mathematica Volume 156 Number 3 (2020), arXiv.1508.05911.
This paper used to be called Taut foliations on graph manifolds.

On the geography and botany of knot Floer homology
(with Matt Hedden)
Selecta Mathematica, Volume 24 Number 2 (2018).

Khovanov homology and the symmetry group of a knot
Advances in Mathematics, Volume 313 (2017).
Accompanying Mathematica notebook for some of the calculations for this paper using KnotTheory`.

The Alexander invariant, Seifert forms, and categorification
(with Jen Hom and Tye Lidman)
Journal of Topology, Volume 10 Number 1 (2017).

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