Classifying fusion categories

March 12 to March 16, 2012

at the

American Institute of Mathematics, San Jose, California

organized by

Scott Morrison, Eric Rowell, and Noah Snyder

Original Announcement

This workshop will be devoted to the classification problem for fusion categories, including those with additional structure, e.g. ribbon and modular fusion categories. More specifically, we will focus on the development and application of both theoretical and computational techniques for classifying fusion categories that are "small" in various senses.

This workshop will bring together interested mathematicians working in Topology, Representation Theory and Subfactor Theory with two main goals:

  1. share techniques and encourage collaborative approaches among these research groups, and
  2. develop hybrid techniques to classification with a view towards establishing a long-term classification program.
Among the interpretations of "small" that will be considered are: small rank, low-dimensional simple objects, bounded global Frobenius-Perron dimension and global Frobenius-Perron dimension having few prime divisors.

Two secondary goals are:

  1. to compile an up-to-date catalog of known classifications and
  2. to search for exotic fusion categories i.e. not related to quantum groups or quasi-Hopf algebras.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop:

Rank finiteness for modular categories
by  Paul Bruillard, Siu-Hung Ng, Eric Rowell, and Zhenghan Wang,  J. Amer. Math. Soc. 29 (2016), no. 3, 857-881  MR3486174
The little desert? Some subfactors with index in the interval (5, 3+\sqrt5)
by  Scott Morrison and Emily Peters,  Internat. J. Math. 25 (2014), no. 8, 1450080, 51 pp  MR3254427
Constructing spoke subfactors using the jellyfish algorithm
by  Scott Morrison and David Penneys,  Trans. Amer. Math. Soc. 367 (2015), no. 5, 3257-3298  MR3314808
An obstruction to subfactor principal graphs from the graph planar algebra embedding theorem
by  Scott Morrison,  Bull. Lond. Math. Soc. 46 (2014), no. 3, 600-608  MR3210716
The classification of subfactors of index at most 5
by  Vaughan F. R. Jones, Scott Morrison, and Noah Snyder,  Bull. Amer. Math. Soc. (N.S.) 51 (2014), no. 2, 277-327  MR3166042
Cyclic extensions of fusion categories via the Brauer-Picard groupoid
by  Pinhas Grossman, David Jordan, and Noah Snyder,  Quantum Topol. 6 (2015), no. 2, 313-331  MR3354332
Classification of integral modular categories of Frobenius-Perron dimension pq^4 and p^2q^2
by  Paul Bruillard, Cesar Galindo, Seung-Moon Hong, Yevgenia Kashina, Deepak Naidu, Sonia Natale, Julia Yael Plavnik, and Eric. C. Rowell,  Canad. Math. Bull. 57 (2014), no. 4, 721–734  MR3270794