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Subfactors of index less than 5, part 3: quadruple points
Joint with Masaki Izumi, Vaughan Jones and Noah Snyder, accepted at Communications in Mathematical Physics, October 8 2011.
pdf · arXiv · blog · project summary
Higher categories, colimits and the blob complex
Joint with Kevin Walker, Proceedings of the National Academy of Sciences May 17, 2011 vol. 108 no. 20 pp. 8139-8145.
pdf · arxiv · journal · project summary
The blob complex
Joint with Kevin Walker, submitted to Geometry & Topology.
pdf · arXiv · Teichner's hot topic course · project summary
Subfactors of index less than 5, part 2: triple points
Joint with David Penneys, Emily Peters and Noah Snyder, in press International Journal of Mathematics.
pdf · arXiv · journal · project summary
Subfactors of index less than 5, part 1: the principal graph odometer
Joint with Noah Snyder, accepted at Communications in Mathematical Physics, June 28 2011.
pdf · arXiv · journal · project summary
Cyclotomic integers, fusion categories, and subfactors
Joint with Frank Calegari and Noah Snyder, Communications in Mathematical Physics Volume 303, Issue 3 (2011), pp. 845-896.
pdf · arXiv · journal · mathscinet · blog · project summary
Non-cyclotomic fusion categories
Joint with Noah Snyder, in press at Transactions of the American Mathematical Society.
pdf · arXiv · blog · project summary
Knot polynomial identities and quantum group coincidences
Joint with Emily Peters and Noah Snyder, Quantum Topology vol. 2 (2011), pp. 101–156.
pdf · arXiv · journal · mathscinet · blog
Constructing the extended Haagerup planar algebra
Joint with Stephen Bigelow, Emily Peters and Noah Snyder, in press at Acta Mathematica.
pdf · arXiv · blog · project summary
Man and machine thinking about the smooth 4-dimensional Poincare conjecture
Joint with Michael Freedman, Robert Gompf and Kevin Walker, Quantum Topology, Volume 1, Issue 2 (2010), pp. 171–208.
pdf · arXiv · journal · blog · mathscinet
The braid group surjects onto G_2 tensor space
Pacific Journal of Mathematics 249-1 (2011), pp. 189-198.
pdf · arxiv · journal · mathscinet
Skein theory for the D_2n planar algebras
Joint with Emily Peters and Noah Snyder, Journal of Pure and Applied Algebra Vol. 214, No. 2 (2010) pp. 117-139.
pdf · arXiv · journal · mathscinet
A Diagrammatic Category for the Representation Theory of U_q(sl_n)
UC Berkeley Ph.D. thesis.
pdf · synopsis · arXiv
Fixing the functoriality of Khovanov homology
Joint with David Clark and Kevin Walker, Geometry and Topology 13 (2009) pp. 1499-1582.
pdf · arXiv · journal · mathscinet
On Khovanov's cobordism theory for su_3 knot homology
Joint with Ari Nieh, Journal of Knot Theory and its Ramifications Vol. 17, No. 9 (2008), pp. 1121-1173.
pdf · arXiv · journal · mathscinet
The Karoubi Envelope and Lee's Degeneration of Khovanov Homology
Joint with Dror Bar-Natan, Algebraic & Geometric Topology 6 (2006) pp. 1459-1469.
pdf · arXiv · journal · mathscinet
Classifying Spinor Structures
BSc. honours thesis at UNSW.
pdf · arXiv

I wrote an opinion piece for the Notices of the American Mathematical Society, about MathOverflow, with Anton Geraschenko and Ravi Vakil.

You might also enjoying reading these notes: The cycloid, Kaleidoscope Eyes October 1997, an elementary derivation of the tautochrone and brachistochrone properties of the cycloid, which I wrote as a high school student.