Classifying fusion categories

March 12 to March 16, 2012

at the

American Institute of Mathematics, Palo Alto, California

organized by

Scott Morrison, Eric Rowell, and Noah Snyder

This workshop, sponsored by AIM and the NSF, 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.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email

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