**Detecting rational maps using
elastic graphs**
(handout, poster)
A lecture at *Dynamical Developments*, a conference in
honor of John Hubbard’s 70th birthday in August, 2015.
There is also an old
version, an invited address at the AMS Sectional Meeting in Eau
Claire, Sept 2014.

**An introduction to Heegaard Floer homology**
Series given at OMGTP XIX in Faro.

- Lecture 1: HF homology from grid diagrams
- Lecture 2: Borderd HF: A toy model
- Lecture 3: Structure of borderd HF homology

**Cluster algebras from surfaces**. Triangulations of
surfaces with at least one puncture provide many examples of
cluster algebras which are *mutationally finite*: there are only
a finite number of different combinatorial types of clusters. We
establish basic properties of the cluster algebras associated
with oriented, bordered surfaces with marked points. We further
show how to introduce coefficients into these cluster algebras
and relate them to the Teichmüller space of the corresponding
hyperbolic surface.

- Lecture 1: Tropical lambda coordinates
- Lecture 2: Hyperbolic geometry and lambda coordinates
- Lecture 3: Constructing cluster algebras from surfaces
- Lecture 4: On canonical bases for surface cluster algebras

Characterizing generic global
rigidity. A framework in **R**^{d} is a graph and a map
from its vertices to **R**^{d}. Such a framework
is *globally rigid* if it is the only framework with the
same edge lengths, up to rigid motions. For which graphs is a
generic framework globally rigid? We answer this by proving a
conjecture of Connelly, that his sufficient condition is also
necessary. Slides from a talk at Columbia. Joint work with
Steven Gortler and Alex Healy.
(PDF,
handout)

Combinatorial link Floer homology and transverse knots, a talk on combinatorial Floer homology, which among other results gives the world's simplest algorithm for computing the knot genus and new examples of knots which are not transversally simple. Joint with/work of Sarkar, Manolescu, Ozsváth, Szabó, and Ng. (source, display, darcs repository, versions from Temple (colloq), Tokyo Inst. of Tech. (expanded))

Computing with Curves on Surfaces, an explanation of the smoothing lemma, a basic tool for working with curves on surfaces, and how to use it to better understand Dehn-Thurston coordinates. (PDF, source, handout)

How efficiently do 3-manifolds bound 4-manifolds? (PDF, source, display), slides from a lecture at the Knots in Vancouver conference at the University of British Columbia, July 23, 2004. Joint work with Francesco Costantino. (Version from Trieste)

Domino tilings and planar algebras generated by a 3-box (PDF, source) slides from a lecture at NCTS in National Tsing Hua University, Taiwan on July 11, 2004.

Shadow surfaces and spines of 3- and 4-manifolds (PDF), notes from a lecture given in Pisa, Italy on June 18, 2003

Hyperbolic volume and the Jones polynomial (PDF), notes from a lecture at MSRI, December 2000. Earlier notes (covering more material) from a lecture series at the Grenoble summer school “Invariants des noeuds et de variétés de dimension 3”, June 1999.

Dylan Thurston Last modified: Sat Jul 2 17:09:58 CEST 2005