Dmitri Nickshych, "How to peel and core a fusion category"
A useful approach to the study of fusion categories
is to understand them up to a Morita equivalence.
It turns out that two fusion categories are Morita equivalent
if and only if their Drinfeld centers are equivalent as braided
categories. Thus one is led to analyze the structure of
such categories. In this talk I will introduce the new invariant
of a braided fusion category C (called the core) which separates
the part of C that does not come from finite groups.
I will describe properties of the core and present
some classification results.
This talk is based on joint works with S. Gelaki, V. Drinfeld,
P. Etingof, and V. Ostrik.