This year, I studied about classification of automorphisms of subfactors in the theory of operator algebras. On one hand, this topic has a close relation to combinatorial aspects of conformal field theory, etc. On the other hand, I have used functional analytic classification theory of Connes fully.
In paper [23], I have shown that approximately inner automorphisms of a strongly amenable AFD II$_1$ subfactor $N\subset M$ are completely classified with my new invariants $(p_a, \gamma_h, \nu)$ when a certain extra condition holds. This kind of classification theory of automorphisms of subfactors was initiated by Loi in 1990, and the strongest form of classification in terms of Loi's invariant was given by Popa in 1992. My new study gives a classification result for the cases with trivial Loi invariant. A motivation for the definitions of the new invariants comes from an analogy between paragroups and flows of weights, proposed by me since 1992. The method of proofs relies on orbifold construction introduced and studied by me in 1990--92, Popa's classification theorem mentioned above, the relative $\chi, \kappa$ invariants introduced by me in 1992--94, and classification theorems of Connes of automorphisms with central sequences.
In particular, my result gives a complete classification of automorphisms of AFD II$_1$ subfactors with index less than four except for one special case. It also gives a complete classification of automorphisms of the Hecke algebra subfactors of Wenzl corresponding to quantum $SU(3)_k$.
Ocneanu's paragroup theory is a great theory linking operator algebras to quantum groups, conformal field theory, and 3-dimensional topology, but many of its fundamental results have been scattered among informal notes, handwritten manuscripts, and fragmentary papers so that the theory has been inaccessible to the general mathematical public except for few experts. I have written book [24] with D. E. Evans on this theory with clarified fundamental results and many applications and examples.