Conformal Field Theory through Subfactors and K-theory

Subfactors and K-theory are useful mechanisms for understanding modular tensor categories and conformal field theories. As part of this programme, one issue to try and construct or reconstruct a conformal field theory as the representation theory of a conformal net of algebras, or as a vertex operator algebra from a given abstractly presented modular tensor category. Orbifold models play an important role and orbifolds of Tambara-Yamagami systems are relevant to understanding the double of the Haagerup as a conformal field theory. This is joint work with Andreas Aaserud, Terry Gannon and Ulrich Pennig.