On the Action of the Symmetric Group on the Cohomology of Groups Related to (Virtual) Braids, arxiv:1304.4645

Proof of a Conjectured Formula for the Alexander Invariant, Journal of Knot Theory and its Ramifications 23 (October, 2014), no. 12; DOI: 10.1142/S0218216514500679. See also arxiv:1209.0668

The Pure Virtual Braid Group Is Quadratic, Selecta Mathematica 19 (2013), no. 2, 461-508; DOI 10.1007/s00029-012-0107-1. See also arxiv:1110.2356.

Closed-Form Associators In Permutative Chord Diagrams, arxiv:1304.4555

Talks

The Pure Virtual Braid Groups and Representation Stability, Seminar, University of Chicago, September 17, 2013. Handout

The Pure Virtual Braid Group is Quadratic, 2012 Spring Eastern Sectional Meeting of the AMS, George Washington University, March 17-18, 2012.

The Pure Virtual Braid Group is Quadratic, Knots in Washington 2012, George Washington University, March 14-16, 2012.

Quadraticity of the Pure Virtual Braid Groups, Algebra Seminar, University of Western Ontario, January 13, 2012. Handout 1Handout 2

Quadraticity of the Pure Virtual Braid Groups, Seminar, University of Bourgogne, December 2, 2011.

The Pure Virtual Braid Group is Quadratic, Algebraic Topology Seminar, University of Strasbourg, November 29, 2011.

A Criterion for Quadraticity of Certain Associated Graded Algebras, Quantum Seminar, University of Strasbourg, November 28, 2011.

Quadraticity of the Pure Virtual Braid Groups, Geometric Representation Theory Seminar, University of Toronto, November 4, 2011.

`Graded' 1-Formality of the Quasi-Triangular Groups, Infinite Dimensional Algebras Seminar, Massachusetts Institute of Technology, October 7, 2011.

A Criterion for the Quadraticity of the Pure Braid Group, Seminar at the University of Geneva Department of Mathematics, May 30, 2011.

Closed-Form Associators in a "Toy" Quotient, Winter 2006 Meeting of the Canadian Mathematical Society, Session on Knot Homologies.
AbstractHandout

A Deformation Quantization Primer, Graduate Student Seminar, Department of Mathematics, University of Toronto, March 23, 2007.
Part 1Part 2Part 3Part 4

Thanks to Dror Bar-Natan for the upper left photo, taken by him at the Winter 2006 Meeting of the Canadian Mathematical Society.

The image of torus knot T(6,5) at the upper right was generated by Dror Bar-Natan and appears at KnotAtlas.