Venice Beach

Liam Watson

Mathematics Department
University of British Columbia


I study problems in low-dimensional 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, left-orders, and non-L-spaces. 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 xwmǝθkwǝy̓ǝm (Musqueam) People.

For 2024-2026 I hold a Killam Accelerator Research Fellowship. I am part of the topology group at UBC, and I am involved in the PIMS CRG Novel Techniques in Low Dimension.

Mathematical Research Postcards is worth checking out.

My office is in Mathematics 219. The best way to contact me is by email: liam[at]math[dot]ubc[dot]ca

Instagram: @mathonmydeskrightnow


My papers on the arXiv, MathSciNet, and zbMATH. These are listed below in (approximate) reverse chronological order.

Preprints and works in preparation

  1. Khovanov multicurves are linear (with Artem Kotelskiy and Claudius Zibrowius)
    Preprint, arXiv.2105.06308.
  2. Khovanov invariants via Fukaya categories: The tangle invariants agree (with Artem Kotelskiy and Claudius Zibrowius)
    Submitted, arXiv.2004.01619.
  3. 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.

Published, in press, or accepted

  1. Thin links and Conway spheres (with Artem Kotelskiy and Claudius Zibrowius)
    To appear in Compositio Mathematica, arXiv.2105.06308.
  2. Cosmetic operations and Khovanov multicurves (with Artem Kotelskiy, Tye Lidman, Allison Moore and Claudius Zibrowius)
    To appear in Mathematische Annalen, arXiv.2109.14049.
  3. Bordered Floer homology for manifolds with torus boundary via immersed curves (with Jonathan Hanselman and Jake Rasmussen)
    To appear in Journal of the American Mathematical Society, arXiv.1604.03466.

    Here is a link to the revised and accepted version of the paper.

    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 low-dimensions.
    Videos of talks on (older versions of) this material from BIRS (2016): Part 1 and Part 2
  4. Heegaard Floer homology for manifolds with torus boundary: properties and examples (with Jonathan Hanselman and Jake Rasmussen)
    To appear in Proceedings of the London Mathematical Society, arXiv.1810.10355.
    Open access link for this paper.

    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).
  5. A mnemonic for the Lipshitz–Ozsváth–Thurston correspondence (with Artem Kotelskiy and Claudius Zibrowius)
    To appear in Algebraic and Geometric Topology, arXiv.2005.02792.
  6. Khovanov homology and strong inversions (with Artem Kotelskiy and Claudius Zibrowius)
    The Open Book Series Volume 5 (2022), arXiv.2104.13592.
    Open access link for this paper.
  7. Cabling in terms of immersed curves (with Jonathan Hanselman)
    Geometry & Topology, Volume 27 Number 3 (2023).
  8. A calculus for bordered Floer homology (with Jonathan Hanselman)
    Geometry & Topology, Volume 27 Number 3 (2023).

    Slides from the EMS/SCM Joint Meetings (2015).
  9. Symmetry & Mutation, Mathematical Research Postcards, Volume 1 Number 1, 2021.

  10. A refinement of Khovanov homology (with Andrew Lobb)
    Geometry & Topology, Volume 25 Number 4 (2021).

    Some additional comments on separating mutants, which simplify/clarify/generalize a construction in this paper, can be found here. These are incorporated into the published version of the paper.
  11. L-spaces, 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.
  12. On the geography and botany of knot Floer homology (with Matt Hedden)
    Selecta Mathematica, Volume 24 Number 2 (2018).
  13. 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`.
  14. The Alexander invariant, Seifert forms, and categorification (with Jen Hom and Tye Lidman)
    Journal of Topology, Volume 10 Number 1 (2017).
  15. Non-fibered L-space knots (with Tye Lidman)
    Pacific Journal of Mathematics, Volume 267, Number 2 (2014).
  16. Genus one open books with non-left-orderable fundamental group (with Yu Li)
    Proceedings of the American Mathematical Society, Volume 142 Number 4 (2014).
  17. Graph manifolds, left-orderability and amalgamation (with Adam Clay and Tye Lidman)
    Algebraic and Geometric Topology, Volume 13, Number 4 (2013).
  18. On L-spaces and left-orderable fundamental groups (with Steve Boyer and Cameron Gordon)
    Mathematische Annalen, Volume 356, Issue 4 (2013).
  19. New proofs of certain finite filling results via Khovanov homology
    Quantum Topology, Volume 4 Number 4 (2013).
  20. Turaev torsion, definite 4-manifolds and quasi-alternating knots (with Josh Greene)
    Bulletin of the London Mathematical Society, Volume 45 Number 5 (2013).
  21. Left-orderable fundamental groups and Dehn surgery (with Adam Clay)
    International Mathematics Research Notices, Number 12 (2013).
  22. Surgery obstructions from Khovanov homology
    Selecta Mathematica Volume 18 Number 2 (2012).

    Slides from my talk at the Georgia Topology Conference.
  23. On cabled knots, Dehn surgery, and left-orderable fundamental groups (with Adam Clay)
    Mathematical Research Letters, Volume 18 Number 6 (2011)
  24. A surgical perspective on quasi-alternating links
    Low-dimensional and Symplectic Topology, Volume 82 of Proceedings of Symposia in Pure Mathematics (2011)
  25. Does Khovanov homology detect the unknot? (with Matt Hedden)
    American Journal of Mathematics, Volume 132 Number 5 (2010).
  26. A remark on Khovanov homology and two-fold branched covers
    Pacific Journal of Mathematics, Volume 245 Number 2 (2010).

    Accompanying Mathematica notebook performing the calculations in this paper using KnotTheory`.
  27. Knots with identical Khovanov homology
    Algebraic and Geometric Topology, Volume 7 (2007).
  28. Simplification of scalar data via monotone-light factorizations (with Martin Brooks)
    Proceedings of the 19th Canadian Conference on Computational Geometry, (2007).
  29. Any tangle extends to non-mutant knots with the same Jones polynomial
    Journal of Knot Theory and its Ramifications, Volume 15 Number 9 (2006).

Edited volumes

  1. Gauge theory and low-dimensional topology: progress and interactions.
    Editors: John Baldwin, Hans Boden, John Etnyre, and Liam Watson
    The Open Book Series Volume 5, 2022.
  2. Characters in low-dimensional topology. A conference celebrating the work of Steven Boyer.
    Editors: Olivier Collin, Cameron Gordon, Stefan Friedl, Stephan Tillmann, and Liam Watson
    Contemporary Mathematics 760. Centre de Recherches Mathématiques Proceedings, 2020.


  1. Involutions on 3-manifolds and Khovanov homology
    UQÀM PhD thesis (June 2009)
    Supervisor: Steve Boyer
  2. Knots, tangles and braid actions
    UBC MSc thesis (October 2004)
    Dale Rolfsen






Glasgow Level 4 Projects


Fall 2018

Winter 2019

Winter 2020

Fall 2020

Winter 2021

Fall 2021

Winter 2022

Winter 2023

Fall 2023

Winter 2024

About this page

The page design for this website was stolen from my friend Patrick Ingram; the photo was taken by Rick Despard at Venice Beach.

Unrelated reading

Communicative Landscapes by Erin Despard.

General awesomness by Elissa Ross.

Silver Bullet Mobility br Karl Saidla.