Venice Beach

Liam Watson

Assistant Professor
Mathematics Department
University of British Columbia




Research

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.

I'm part of the topology group at UBC. Our seminar meets Wednesdays from 2:45 to 3:45 at PIMS. In addition, I am running a working group this term, which meets on Thursdays from 2:00 to 4:00 (also at PIMS).

If you are on the postdoctoral job market this year, UBC has posted positions on mathjobs here. Please apply!

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

  1. Heegaard Floer homology for manifolds with torus boundary: properties and examples (with Jonathan Hanselman and Jake Rasmussen)
    Preprint, 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).
  2. 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 low-dimensions.
    Videos of talks on (older versions of) this material from BIRS (2016): Part 1. and Part 2
  3. Taut foliations on graph manifolds (with Jonathan Hanselman, Jake Rasmussen and Sarah Rasmussen)
    Submitted, arXiv.1508.05911.
  4. 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

  1. On the geography and botany of knot Floer homology (with Matt Hedden)
    Selecta Mathematica, Volume 24 Number 2 (2018).
  2. 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`.
  3. The Alexander invariant, Seifert forms, and categorification (with Jen Hom and Tye Lidman)
    Journal of Topology, Volume 10 Number 1 (2017).
  4. Non-fibered L-space knots (with Tye Lidman)
    Pacific Journal of Mathematics, Volume 267, Number 2 (2014).
  5. Genus one open books with non-left-orderable fundamental group (with Yu Li)
    Proceedings of the American Mathematical Society, Volume 142 Number 4 (2014).
  6. Graph manifolds, left-orderability and amalgamation (with Adam Clay and Tye Lidman)
    Algebraic and Geometric Topology, Volume 13, Number 4 (2013).
  7. On L-spaces and left-orderable fundamental groups (with Steve Boyer and Cameron Gordon)
    Mathematische Annalen, Volume 356, Issue 4 (2013).
  8. New proofs of certain finite filling results via Khovanov homology
    Quantum Topology, Volume 4 Number 4 (2013).
  9. Turaev torsion, definite 4-manifolds and quasi-alternating knots (with Josh Greene)
    Bulletin of the London Mathematical Society, Volume 45 Number 5 (2013).
  10. Left-orderable fundamental groups and Dehn surgery (with Adam Clay)
    International Mathematics Research Notices, Number 12 (2013).
  11. Surgery obstructions from Khovanov homology
    Selecta Mathematica Volume 18 Number 2 (2012).

    Slides from my talk at the Georgia Topology Conference.
  12. On cabled knots, Dehn surgery, and left-orderable fundamental groups (with Adam Clay)
    Mathematical Research Letters, Volume 18 Number 6 (2011)
  13. A surgical perspective on quasi-alternating links
    Low-dimensional and Symplectic Topology, Volume 82 of Proceedings of Symposia in Pure Mathematics (2011)
  14. Does Khovanov homology detect the unknot? (with Matt Hedden)
    American Journal of Mathematics, Volume 132 Number 5 (2010).
  15. 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`.
  16. Knots with identical Khovanov homology
    Algebraic and Geometric Topology, Volume 7 (2007).
  17. Simplification of scalar data via monotone-light factorizations (with Martin Brooks)
    Proceedings of the 19th Canadian Conference on Computational Geometry, (2007).
  18. Any tangle extends to non-mutant knots with the same Jones polynomial
    Journal of Knot Theory and its Ramifications, Volume 15 Number 9 (2006).

Theses

  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)
    Supervisor:
    Dale Rolfsen

Supervision

Postdoctoral

Doctoral

Masters

Undergraduate

Glasgow Level 4 Projects

Teaching

Fall 2018

Winter 2019

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.