Feng Xu

Abstract:   In this talk we will describe a mathematical framework where a strong interaction exists between conformal field theories (CFT) and operator algebras, especially index theory of subfactors. On the operator algebra side we obtain large classes of interesting subfactors from CFT, including many exotic subfactors which have played roles in the formulation of boundary states (D-branes). On CFT side the operator algebraic approach among other things is particularly effective in the case of orbifolds and cosets, which are two important constructions in CFT. We will describe some recent results in this direction, which so far have not been obtained by other methods.