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A field guide to categories with $A_n$ fusion rules.
Joint with Cain Edie-Michell
pdf · arxiv
Lifting shadings on symmetrically self-dual subfactor planar algebras.
Joint with Zhengwei Liu and David Penneys.
pdf · arxiv
Monoidal categories enriched in braided monoidal categories.
Joint with David Penneys.
pdf · arxiv · journal
Modular data for the extended Haagerup subfactor.
Joint with Terry Gannon.
pdf · arxiv · journal
The classification of subfactors with index at most $5 \frac{1}{4}$.
Joint with Narjess Afzaly and David Penneys.
pdf · arxiv
Computing annular Khovanov homology.
Joint with Hilary Hunt, Hannah Keese, and Anthony Licata.
pdf · arxiv
Categories generated by a trivalent vertex.
Joint with Emily Peters and Noah Snyder, Selecta Mathematica 2016.
pdf · arxiv · journal · Emily's talk at IPAM · google scholar · scopus
2-supertransitive subfactors at index $3+\sqrt{5}$.
Joint with David Penneys, Journal of Functional Analysis 269 (2015), pp. 2845-2870.
pdf · arxiv · journal · mathscinet · google scholar · scopus
Subfactors of index exactly 5.
Joint with Masaki Izumi, David Penneys, Emily Peters, and Noah Snyder, Bulletin of the London Mathematical Society (2015) 47 (2), pp. 257-269.
pdf · arxiv · journal · mathscinet · google scholar · scopus · web-of-science
The centre of the extended Haagerup subfactor has 22 simple objects.
Joint with Kevin Walker, International Journal of Mathematics, 28, 1750009 (2017).
pdf · arxiv · article google scholar
1-supertransitive subfactors with index at most $6\frac{1}{5}$
Joint with Zhengwei Liu and David Penneys, Communications in Mathematical Physics 334 (2015), issue 2, pp. 889-922.
pdf · arxiv · journal · mathscinet · google scholar · scopus · web-of-science
Quotients of $A_2 * T_2$
Joint with Masaki Izumi and David Penneys, Canadian Journal of Mathematics 68 (2016), no. 5, 999-1022.
journal · google scholar
Extended version "Fusion categories between $C \boxtimes D$ and $C * D$":
arxiv · pdf
The classification of subfactors of index at most 5
Joint with Vaughan F. R. Jones and Noah Snyder, Bulletin of the American Mathematical Society 51 (2014), no. 2, pp. 277-327.
pdf · arxiv · journal · mathscinet · google scholar · scopus · web-of-science
An obstruction to subfactor principal graphs from the graph planar algebra embedding theorem
Bulletin of the London Mathematical Society, 46 (2014) pp. 600–608.
pdf · arxiv · journal · mathscinet · google scholar · scopus · web-of-science
Webs and quantum skew Howe duality
Joint with Sabin Cautis and Joel Kamnitzer, Mathematische Annalen, October 2014, Volume 360, Issue 1-2, pp. 351-390.
pdf · arxiv · journal · mathscinet · google scholar · scopus · web-of-science
Constructing spoke subfactors using the jellyfish algorithm
Joint with David Penneys, Transactions of the American Mathematical Society vol. 367, no. 5, pp. 3257--3298 (2015).
pdf · arXiv · journal · mathscinet · project summary · google scholar · scopus · web-of-science
The little desert? Some subfactors with index in the interval $(5,3+\sqrt{5})$
Joint with Emily Peters, International Journal of Mathematics vol. 25, 1450080 (2014).
pdf · arXiv · journal · mathscinet · project summary · google scholar · scopus · web-of-science
Subfactors of index less than 5, part 3: quadruple points
Joint with Masaki Izumi, Vaughan F. R. Jones and Noah Snyder, Communications in Mathematical Physics, vol. 316, issue 2 (2012), pp. 531-554.
pdf · arXiv · journal · mathscinet · blog · project summary · google scholar · scopus · web-of-science
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 · mathscinet · project summary · google scholar · scopus · web-of-science
Blob homology
Joint with Kevin Walker, Geometry & Topology 16 (2012) 1481-1607.
pdf · arXiv · journal · mathscinet · Teichner's hot topic course · project summary · google scholar · scopus · web-of-science
Subfactors of index less than 5, part 2: triple points
Joint with David Penneys, Emily Peters and Noah Snyder, International Journal of Mathematics Vol. 23, No. 3 (2012) 1250016 (33 pages).
pdf · arXiv · journal · mathscinet · project summary · google scholar · scopus · web-of-science
Subfactors of index less than 5, part 1: the principal graph odometer
Joint with Noah Snyder, Communications in Mathematical Physics, vol. 312, issue 1 (2012), pp. 1-35.
pdf · arXiv · journal · mathscinet · project summary · google scholar · scopus · web-of-science
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 · google scholar · scopus · web-of-science
Non-cyclotomic fusion categories
Joint with Noah Snyder, Transactions of the American Mathematical Society 364 (2012), no. 9, 4713–4733.
pdf · arXiv · journal · mathscinet · blog · project summary · google scholar · scopus · web-of-science
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 · google scholar
Constructing the extended Haagerup planar algebra
Joint with Stephen Bigelow, Emily Peters and Noah Snyder, Acta Mathematica, vol. 209 (2012), pp. 29--82.
pdf · arXiv · journal · mathscinet · blog · project summary · google scholar · scopus · web-of-science
Man and machine thinking about the smooth 4-dimensional Poincare conjecture
Joint with Michael Freedman, Robert Gompf and Kevin Walker, Quantum Topology, vol. 1, issue 2 (2010), pp. 171–208.
pdf · arXiv · journal · blog · mathscinet · google scholar
The braid group surjects onto $G_2$ tensor space
Pacific Journal of Mathematics 249-1 (2011), pp. 189-198.
pdf · arxiv · journal · mathscinet · google scholar · scopus · web-of-science
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 · google scholar · scopus · web-of-science
A Diagrammatic Category for the Representation Theory of $U_q(\mathfrak{sl}_n)$
UC Berkeley Ph.D. thesis.
pdf · synopsis · arXiv · google scholar · web-of-science
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 · google scholar · scopus · web-of-science
On Khovanov's cobordism theory for $\mathfrak{su}_3$ 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 · google scholar · scopus · web-of-science
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 · google scholar · web-of-science
A formula for the Jones-Wenzl projections
Proceedings of the 2014 Maui and 2015 Qinhuangdao conferences in honour of Vaughan F.R. Jones’ 60th birthday
pdf · arXiv · proceedings mathscinet · google scholar
Classifying Spinor Structures
BSc. honours thesis at UNSW.
pdf · arXiv · google scholar

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.


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