Subfactors of the hyperfinite II1 factor of index less than or equal to 4 were classified in the late 80s and early 90s through work of Jones, Ocneanu, Popa, and many others. There is an ADE classification, and all of the examples are closely related to quantum or classical SU(2). When the index is larger than 4, there is one family of A∞ subfactors related to quantum SU(2) which are difficult ...