Operator Algebras and Conformal Field Theories

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AbstractXuThe PI will study interactions between operator algebras and conformalfield theories which have proved to be very fruitful lately. The mainemphasis of this research is placed on the study of certain representation theoryquestions such as Kac-Wakimoto conjecture, orbifolds and boundary states in conformal field theories using operator algebraic techniques. The applications of these operator algebraic techniqueswill lead to proofs of representation theory questionsand shed lights on exotic subfactors such as those coming from conformal inclusions. The theory of operator algebras was introduced by John von Neumann in order to provide a proper mathematical framework for Quantum Mechanics. Conformal field theory was a theory describing critical phenomena incondensed matter physics, and it also plays an important role in string theory. The remarkable interactions between operator algebrasand conformal field theory has led to many interesting mathematicalissues. The aim of this researchis to find solutions to some of the important mathematical issues that surface in this context which have a wide range of applications.