# Mathematics Colloquia and Seminars

### A classification of fusion categories generated by an object of dimension $(1+\sqrt5)/2$
The celebrated Jones index theorem implies that if the dimension of an object in a unitary fusion category is less than 2, then it is of the form $2\cos (\pi/n)$ for $n$ a natural number. Further, each of these dimensions is realized by at least one example. A natural extension of this theorem is to ask for the classification of all objects of dimension less than 2 that can appear in unitary fusion categories. In this talk I will answer this question for the third-smallest dimension in a unitary fusion category, $(1+\sqrt5)/2$.