Title: Classifying fusion categories generated by an object of small dimension.
Speaker: Cain Edie-Michell (Vanderbilt University)
Abstract: One of the main goals in the study of fusion categories is to provide a complete classification result. However at the current time not even a conjectural description of all fusion categories has been given. Because a complete classification is completely out of reach with current techniques, current research on fusion categories focuses on classifying ``small” fusion categories, where small can have a variety of different meanings. For this talk, small will mean generated by an object of small Frobenius-Perron dimension. I will discuss a recent partial classification result of mine along these lines. I assume the generating object has dimension less than 2, along with a mild assumption on the commutativity of the generating object. This classification contains some very surprising categories, including some exceptional quantum subgroups.