Notes for Morrison-140220/0:00:00

Abstract. The 2-dimensional extended TFTs correspond to fusion categories. We know constructions of fusion categories from finite group data and from quantum groups at roots of unity, but what else is out there? We are very far from having satisfying answers, but have now approached the problem from several different directions. I will explain some of the notions of a 'small' fusion category, and describe what we've seen so far. Some examples, in particular the fusion categories coming from the Haagerup subfactor, appear over and over again. I suspect that 'eventually' there will be an unmanageable surfeit of sporadic fusion categories, but so far efforts at classification have turned up surprisingly few instances.