# The representation theory of a subfactor

SPEAKER: David Penneys

TITLE: The representation theory of a subfactor

ABSTRACT The representation theory of a finite index subfactor is a certain unitary 2-category with nice duals. If the subfactor is finite depth, this 2-category gives a Morita equivalence of two fusion categories. These fusion categories allow us to apply strong number theoretic results to subfactor theory. In particular, Etingof-Nikshych-Ostrik showed that the index of a finite index, finite depth subfactor must lie in a cyclotomic field. I will describe recent joint work with Tener to automate a number theoretic result of Calegari-Morrison-Snyder, which together with this theorem of ENO, eliminates vines in the classification of subfactors with index less than 5. This talk will not rely on my talk in the analysis seminar.