Characterizing generic global rigidity. A framework in Rd is a graph and a map from its vertices to Rd. 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. (PDF, source, display, darcs repository, versions from Cornell, Georgia, Princeton, Nankai, Hanoi, Rice, Harvard)
Computing with Curves on Surfaces, slides from a lecture at the Workshop on Computational Geometry and Topology in FoCM'05 in Santander, Spain, July 2, 2005.
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.