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- my publications on the arXiv
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One of my major research interests is in fusion categories and subfactors.

With Masaki Izumi, Vaughan Jones, David Penneys, Emily Peters, Noah Snyder and James Tener, I have recently completed the classification of subfactors with index less than 5. This classification is described in our survey paper- The classification of subfactors of index at most 5
- Joint with Vaughan F. R. Jones and Noah Snyder
- pdf · arxiv

- 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
- 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
- Subfactors of index less than 5, part 3: quadruple points
- Joint with , Vaughan Jones and Noah Snyder, accepted at
*Communications in Mathematical Physics*, October 8 2011. - pdf · arXiv
- Subfactors of index less than 5, part 4: vines
- Written David Penneys and James Tener,
*International Journal of Mathematics*, Vol. 23, No. 3 (2012) 1250017 (18 pages). - pdf · arXiv · journal

- An obstruction to subfactor principal graphs from the graph planar algebra embedding theorem
- pdf · arxiv
- Constructing spoke subfactors using the jellyfish algorithm
- Joint with David Penneys, to appear
*Transactions of the American Mathematical Society*. - pdf · arXiv · project summary
- The little desert? Some subfactors with index in the interval $(5,3+\sqrt{5})$
- Joint with
- pdf · arXiv

- November 30 2011,
**Non-commutative Galois theory and the classification of small-index subfactors**, by Emily Peters, University of Massachussetts, Boston. (slides) - October 29 2011,
**Connections and planar algebras**, Von Neumann algebras and Conformal Field Theory at Vanderbilt. (abstract) - October 19 2011,
**Small index subfactors**, Toronto colloquium. (abstract, prezi) - October 8,
**Classifying fusion categories and subfactors**, SIAM Mini-symposium on Algebraic Aspects of Quantum Computing, Raleigh. (slides) - September 24 2011,
**The classification of small-index subfactors**, by Emily Peters, Wabash extramural modern analysis miniconference. (slides) - May 27 2011,
**The classification of subfactors up to index 5**, by Emily Peters, IHP conference on "$II_1$ factors: rigidity, symmetries and classification". (slides) - May 20 2011,
**Classifying small index subfactors**, Great Plains Operator Theory Symposium. (slides, prezi) - Match 24 2011,
**Finite quantum groups**, by Noah Snyder, Vanderbilt Colloquium. (slides) - January 13 2011,
**Fusion categories and subfactors**, UCSD Colloquium. (slides, prezi) - January 8 2011,
**Eliminating weeds and vines in the classification of subfactors to index 5**, by David Penneys, AMS Joint Meetings in New Orleans. (slides) - November 10 2010,
**Fusion categories and subfactors**, Caltech Colloquium. (slides, prezi) - October 29 2010,
**Classifying subfactors up to index 5**, Kyoto Operator Algebra seminar. (slides) - October 24 2010,
**Classification of subfactors**, by Emily Peters, ECOAS 2010 (slides) - October 8 2010,
**Subfactors at index 5 and beyond**, UCLA/DARPA subfactors meeting. (slides) - September 2 2010,
**Classification of subfactors up to index 5.**Quantum groups, Clermont-Ferrand. (prezi) - August 11 2010,
**Classification of subfactors up to index 5.**Operator algebras satellite conference, Chennai (prezi) - June 4 2010,
**Classifying fusion categories.**Miller Institute Symposium. (poster) - May 11 2010,
**Classification of subfactors up to index 5.**, Non-commutative geometry and operator algebras, Vanderbilt. (prezi) - October 18 2009,
**Fusion categories and small index subfactors, part I**, by Noah Snyder, special session on Fusion Categories at AMS Waco meeting. (slides) - October 18 2009,
**Fusion categories and small index subfactors, part II**, special session on Fusion Categories at AMS Waco meeting. (slides) - September 3 2009,
**Fusion categories**, UC Berkeley Colloquium. (blackboards) - June 3 2009,
**Classifying subfactor planar algebras**, UC Riverside colloquium.

- 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

- Constructing the extended Haagerup planar algebra
- Joint with Stephen Bigelow, Emily Peters and Noah Snyder, in press at
*Acta Mathematica*. - pdf · arXiv

- March 22,
**Extended Haagerup exists!**, Tensor Categories in Bloomington, Indiana.

- April 20 2011,
**Knots, the Four-color Theorem, and von Neumann Algebras**, D.W. Weeks seminar at MIT. (slides) - October 17 2009,
**Constructing the extended Haagerup subfactor**, WCOAS 2009, Reno. (slides)

- Non-cyclotomic fusion categories
- Joint with Noah Snyder, in press at
*Transactions of the American Mathematical Society*. - pdf · arXiv