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Kashaev-Reshetikhin Invariants of Links.
Joint with Kai-Chieh Chen, Calvin McPhail-Snyder, and Noah Snyder
pdf · arxiv
Schemes in Lean.
Joint with Kevin Buzzard, Chris Hughes, Kenny Lau, Amelia Livingston, and Ramon Fernández Mir
Published online 25 Nov 2021 in Experimental Mathematics.
pdf · arxiv · journal
Extension theory for braided-enriched fusion categories.
Joint with Corey Jones, David Penneys, and Julia Plavnik
To appear in the International Mathematics Research Notices,
pdf · arxiv
Invariants of 4-manifolds from Khovanov-Rozansky link homology.
Joint with Kevin Walker and Paul Wedrich
To appear Geometry and Topology
pdf · arxiv
Rank-finiteness for G-crossed braided fusion categories.
Joint with Corey Jones, Dmitri Nikshych, and Eric C. Rowell
Transform. Groups 26, No. 3, 915-927 (2021).
pdf · arxiv · journal
The Extended Haagerup fusion categories.
Joint with Pinhas Grossman, David Penneys, Emily Peters, and Noah Snyder
Accepted 26 Jun 2021 in Annales scientifiques de l'École normale supérieure.
pdf · arxiv
Completion for braided enriched monoidal categories.
Joint with David Penneys, Julia Plavnik
pdf · arxiv
Computing Modular Data for Pointed Fusion Categories.
Joint with Angus Gruen
Indiana Univ. Math. J. 70, No. 2, 561-593 (2021).
pdf · arxiv · journal
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, accepted Contemporary Mathematics, Proceedings of the AMS Special Session on Topological Phases of Matter and Quantum Computation, Feb 2018.
pdf · arxiv
Monoidal categories enriched in braided monoidal categories.
Joint with David Penneys, International Mathematics Research Notices, October 2017
pdf · arxiv · journal
Modular data for the extended Haagerup subfactor.
Joint with Terry Gannon, Communications in Mathematical Physics December 2017, Volume 356, Issue 3, pp 981–1015.
pdf · arxiv · journal
The classification of subfactors with index at most $5 \frac{1}{4}$.
Joint with Narjess Afzaly and David Penneys.
To appear in the Memoirs of the American Mathematical Society
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.
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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.
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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.
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An obstruction to subfactor principal graphs from the graph planar algebra embedding theorem
Bulletin of the London Mathematical Society, 46 (2014) pp. 600–608.
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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.
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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.
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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.
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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.
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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.
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The braid group surjects onto $G_2$ tensor space
Pacific Journal of Mathematics 249-1 (2011), pp. 189-198.
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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.
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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.
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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.
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The Karoubi Envelope and Lee's Degeneration of Khovanov Homology
Joint with Dror Bar-Natan, Algebraic & Geometric Topology 6 (2006) pp. 1459-1469.
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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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