Spanish Banks

Liam Watson

Reader
University of Glasgow
School of Mathematics and Statistics

I am part of the Geometry and Topology group in Glasgow; I am a co-organizer of the weekely G&T seminar.

Before moving to Glasgow I spent 4 years at UCLA; I completed my PhD at UQÀM in 2009. More details can be found in my CV.

My research is supported by a Marie Curie Career Integration Grant.

My office is room 334 of the Maths Building.

My email is: Liam [dot] Watson [at] glasgow [dot] ac [dot] uk

Current

The LMS/CMI summer school Developments in Contact and Symplectic Topology will be held in Glasgow June 20 to 24, 2016. Registration is now closed.

The 31st British Topology Meeting runs August 29 to 31 in Glasgow.

There will be a 6 month program at the Isaac Newton Institute in Cambridge on Homology Theories in Low Dimensional Topology in 2017. I am an organizer, along with Dorothy Buck, Andrew Lobb, and Jake Rasmussen.

Joseph MacColl's work from his Carnegie summer project Rotors in Khovanov homology is on the arXiv (arxiv.org/abs/1501.00851) and has been accepted for publication in Canadian Mathematical Bulletin. More here.

Kathryn Elmer and I have been awarded a Lord Kelvin Adam Smith studentship for the project Convergence, connectivity, and continuity - Topological perspectives for mining novel biological information from ‘omics data.

The workshop an afternoon in low-dimensions, Glasgow (March 20, 2015) included speakers Jonathan Hanselman (UT Austin) and Jake Rasmussen (Cambridge).

Research

My area of research is low-dimensional 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).

L-spaces and left-orderability
The simplest three-manifolds, from the vantage point of Heegaard Floer theory, are L-spaces. These come up in application and satisfy interesting properties, but a complete understanding of L-spaces is lacking. However, there appear to be strong connections with foliations and left-orderable 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

  1. Bordered Floer homology for manifolds with torus boundary via immersed curves
    (with Jonathan Hanselman and Jake Rasmussen)
    Preprint, arXiv.1604.03466.
  2. Taut foliations on graph manifolds
    (with Jonathan Hanselman, Jake Rasmussen and Sarah Rasmussen)
    Submitted, arXiv.1508.05911.
  3. A calculus for bordered Floer homology (with Jonathan Hanselman)
    Submitted, arXiv.1508.05445.
    Slides from the EMS/SCM Joint Meetings (2015)
  4. 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`.
  5. Heegaard Floer homology solid tori (with Jonathan Hanselman)
    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).
  6. The Alexander invariant, Seifert forms, and categorification (with Jen Hom and Tye Lidman)
    Submitted, arXiv:1501.04866.
  7. On the geography and botany of knot Floer homology (with Matt Hedden)
    Submitted, arXiv:1404.6913.

Published, in press, or accepted

  1. Non-fibered L-space knots (with Tye Lidman)
    Pacific Journal of Mathematics, Volume 267, Number 2 (2014).
  2. Genus one open books with non-left-orderable fundamental group (with Yu Li)
    Proceedings of the American Mathematical Society, Volume 142 Number 4 (2014).
  3. Graph manifolds, left-orderability and amalgamation (with Adam Clay and Tye Lidman)
    Algebraic and Geometric Topology, Volume 13, Number 4 (2013).
  4. On L-spaces and left-orderable fundamental groups (with Steve Boyer and Cameron Gordon)
    Mathematische Annalen, Volume 356, Issue 4 (2013).
  5. New proofs of certain finite filling results via Khovanov homology
    Quantum Topology, Volume 4 Number 4 (2013).
  6. Turaev torsion, definite 4-manifolds and quasi-alternating knots (with Josh Greene)
    Bulletin of the London Mathematical Society, Volume 45 Number 5 (2013).
  7. Left-orderable fundamental groups and Dehn surgery (with Adam Clay)
    International Mathematics Research Notices, Number 12 (2013).
  8. Surgery obstructions from Khovanov homology
    Selecta Mathematica Volume 18 Number 2 (2012).
    Slides from my talk at the Georgia Topology Conference.
  9. On cabled knots, Dehn surgery, and left-orderable fundamental groups (with Adam Clay)
    Mathematical Research Letters, Volume 18 Number 6 (2011)
  10. A surgical perspective on quasi-alternating links
    Low-dimensional and Symplectic Topology, Volume 82 of Proceedings of Symposia in Pure Mathematics (2011)
  11. Does Khovanov homology detect the unknot? (with Matt Hedden)
    American Journal of Mathematics, Volume 132 Number 5 (2010).
  12. 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`.
  13. Knots with identical Khovanov homology
    Algebraic and Geometric Topology, Volume 7 (2007).
  14. Simplification of scalar data via monotone-light factorizations (with Martin Brooks)
    Proceedings of the 19th Canadian Conference on Computational Geometry, (2007).
  15. 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

Other writing

  1. Simplification of sampled scalar fields by removal of extrema (with Martin Brooks)
    NRC Technical Report (2007).

Student supervision

Doctoral

Masters

Undergraduate

Glasgow Level 4 Projects

Teaching

About this page

The page design for this website was stolen from my friend Patrick Ingram; the photo was taken at Spanish Banks in Vancouver, early in the morning, by my friend Andrew Rowat.

Unrelated reading

Communicative landscapes by Erin Despard.