Subfactor theory and fusion categories

I will give an introduction to the connections between subfactor theory, a subject in functional analysis, more specifically the theory of von Neumann algebras, and fusion categories, a special class of monoidal categories. Understanding the connections between the two subjects has led to considerable progress in the latter theory, examples being provided by the notion of 'monoidal Morita equivalence' of fusion categories and the recent results on the Drinfeld center of fusion categories.