Orbifold subfactors have been first described by Y. Kawahigashi as an application of paragroup theory. It is known that subfactors of type D_4n and D_4n+2 give rise to fusion algebras of bimodules with different natures, but the origin of the difference is unknown. Asaeda has been working on this problem, and obtained the clue to clarify the fusion structure of orbifold subfactors. On this research, the relation between the representation theory of classical Lie group and that of quantum group (WZW model) plays a crucial role. Her research includes further research on this matter, and clarification of the relation between orbifold of WZW model, structure of the representation of the classical Lie groups, and the nature of subfactors arising from WZW model. On the other hand, her research extends to the study of subfactors which are not arising from quantum groups or classical groups. These subfactors are called exotic subfactors. Her focus is on the structure of quantum double constructed from exotic subfactors. The theory of operator algebras was founded by von Neumann as a mathematical background of quantum mechanics. Lately the relation among operator algebras, quantum physics, and low dimensional topology has been sought from the aspect that is totally different from that of von Neumann. The research on this subject and it's relation with other subjects will contribute the development of many subjects in mathematics and mathematical physics.
