Ocneanu will investigate three classes of problems. The first class to be investigated concern the general discrete structure behind the rigidity results of finite depth subfactors; the second class of problems concerns the introduction and use of the new technical tools for subfactors such as the maximal atlas, the generalized intermediate subfactors and the modular matrices associated to a subfactor; and the third class of problems concerns the detailed study of concrete classes of examples such as the maximal atlas of cross products by a group, the structure of connections between Coxeter graphs, and the structure of connections between affine Coxeter graphs.
This research is in the area of operator algebras, which can be thought of as the infinite dimensional analogue of the algebra of n-dimensional square matrices. This subject had its origins in the early efforts to give a rigorous mathematical foundation to quantum mechanics, and there is still a rich symbiosis between the two subjects.
