My publications as of 2020

• 01 "Supplements of bounded permutation groups", Journal of Symbolic Logic, 1998.
• 02 "The Burau representation is not faithful for n=5", Geometry and Topology, 1999.
• 03 "Braid groups are linear", Journal of the American Mathematical Society, 2000.
• 03.14 I contributed to a problem list.
• 04 "The mapping class group of a genus two surface is linear", with Ryan Budney, Algebraic and Geometric Topology, 2001.
• 05 "Does the Jones polynomial detect the unknot?", Journal of Knot Theory and its Ramifications, 2002.
• 06 "A homological definition of the Jones polynomial", Geometry and Topology Monographs, 2002.
• 07 "Representations of braid groups", Proceedings of the International Congress of Mathematics, 2002.
• 08 "The Lawrence-Krammer representation", Topology and Geometry of Manifolds, 2003.
• 09 "Homological representations of the Iwahori-Hecke algebra", Geometry and Topology Monographs, 2004.
• 10 "Braid groups and Iwahori-Hecke algebras", Proceedings of Symposia in Pure Mathematics, 2006.
• 11 "A homological definition of the HOMFLY polynomial", Algebraic and Geometric Topology, 2007.
• 12 "Generalized Long-Moody representations of braid groups", with Jianjun Paul Tian, Communications in Contemporary Mathematics, 2008.
• 13 "Skein theory for the ADE planar algebras", Journal of Pure and Applied Algebra, 2010.
• 14 "A diagrammatic Alexander invariant of tangles", Journal of Knot Theory and its Ramifications, 2012.
• 15 "The Alexander and Jones polynomials through representations of rook algebras", with Eric Ramos and Ren Yi, JKTR, 2012.
• 16 "Constructing the extended Haagerup planar algebra", with Scott Morrison, Emily Peters and Noah Snyder, Acta Mathematica, 2012.
• 17 "Principal graph stability and the jellyfish algorithm", with David Penneys, Mathematische Annalen, 2014.
• 18 "A diagrammatic definition of Uqsl2", Journal of Knot Theory and its Ramifications, 2014.
• 19 "Alexander representation of tangles", with Alessia Cattabriga and Vincent Florens, Acta Mathematica Vietnamica, May 2015,
• 20 "The pop-switch planar algebra and the Jones-Wenzl idempotents", with Ellie Grano, Journal of Knot Theory and its Ramifications, June 2015. (A "featured article" for 2015!)
• 21 "Bowling ball representations of braid groups", Journal of Knot Theory and its Ramifications, March 2018.
• 22 "An exact entangling gate Using Fibonacci anyons" with Claire Levaillant, Bulletin of the Australian Mathematical Society, November 2018.
• C-1 An entry in The Concise Encyclopedia of Knot Theory
• C-2 "On the Burau representation of B4 modulo p", with Beridze and Traczyk.
• C-3 "Review: the annular structure of subfactors, by Vaughan Jones".
• C-3 "A new approach to the SLn spider".

Errata

I keep a list of errors and regrettable choices from my published papers. Let me know if you find more!

• [02] The Burau representation is not faithful for n=5: I called the full twist braid Δ, but the usual name is Δ². Also, the paper includes a URL that, not surprisingly, doesn't work anymore.
• [03] Braid groups are linear: Theorem 4.1, which gives the matrix entries for the faithful representation, contains a sign error.
• [05] Does the Jones polynomial detect the unknot? I slightly regret the title, since the paper is mostly about Burau-4. Also I regret saying "In the case of B3, I know of no other value of q other than roots of unity at which the Burau representation is unfaithful". This was technically true at the time, but I should have known that such values are easy to find.
• [09] Homological representations of the Iwahori-Hecke algebra: In the statement of Lemma 3.1, "n+k-1 choose k" should be "n+k-2 choose k".
• [11] A homological definition of the HOMFLY polynomial: I slightly regret the title, since this is actually a homological definition of the SLn invariants.
• [12] Generalized Long-Moody representations of braid groups: Somebody pointed out an error but I have forgotten what it was. Probably a sign error, or something acting on the wrong side, or something like that.
• [13] Skein theory for the ADE planar algebras: The proof of Lemma 3.2 did not say why R generates P'. (It's because R generates the minimal projectors.) The proof of Lemma 4.5 has a greater-than symbol that should be less-than.
• [17] Principal graph stability and the jellyfish algorithm: In the diagram in Remark 2.9, the "n+1" should be "n", and the corresponding "n" should be "n-1".
• [18] A diagrammatic definition of Uqsl2: Section 6 constructs a quotient of H by a certain intersection of kernels. However it is not clear that this intersection of kernels is a Hopf ideal. As a workaround, you can quotient by the specific generators that I want to get rid of, and notice that the result still has a well-defined Hopf algebra structure. Vijay Higgins told me he thinks he can fix my original approach.
• [20] The pop-switch planar algebra and the Jones-Wenzl idempotents: In the definition of the pop-switch relations, the first equation is correct, but the second is not. It should be what you get by reversing all of the arrows in the first equation.