Subfactors and Fusion Categories (14w5083)


Vaughan Jones (Vanderbilt University)

(Australian National University)


(Northwestern University)

(Indiana University)


The Banff International Research Station will host the "Subfactors and Fusion Categories" workshop from April 13th to April 18th, 2014.

Symmetry has long played a key role in mathematics and the sciences. Classically, the symmetries of an object form a group. In the past few decades it has become clear that in certain “quantum” settings the notion of group doesn’t capture all possible symmetries. One very early place that these more general symmetries were observed was in the study of von Neumann factors. These quantum analogues of finite groups are called fusion categories. It turns out that these kinds of quantum symmetries turn up in other places in mathematics, like knot theory and representation theory. Surprisingly, fusion categories also crop up in solid state physics, where they govern the behavior of certain exotic materials which may be useful in quantum computing. The aim of this workshop is to bring together experts working on subfactors and fusion categories. With both of these fields developing in new and interesting directions, our goal is to build stronger connections and bridge the gaps between the languages and techniques used by the two communities. We will work towards gaining as rich an understanding of these finite quantum groups as we have of ordinary finite groups.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).