Organizing Braided Fusion Categories

Braided fusion categories encode data from such diverse areas of mathematics as quantum computation, representation theory, topological quantum field theory, knot theory, von Neumann algebras, and other assorted topics in mathematical physics.  We will discuss the extent to which these categories have been classified, a variety of tools which have been constructed for this purpose, and optimistically conjecture about progress in the near future.

If you have studied the representation theory of finite groups, then you will be able to relate to a good portion of this talk.