Operator Algebras and Algebraic Conformal Field Theories

PI将研究算子代数和共形场论之间的相互作用，这些理论最近被证明是非常富有成果的。本研究的主要重点是放在某些表示论问题的研究，如卡茨Wakimoto猜想，orbifolds和边界状态的共形场论使用算子代数技术。 这些算子代数技术的应用将导致证明表示论的问题，并揭示了异国情调的子因子，如那些来自共形夹杂物。算子代数理论是由约翰·冯·诺依曼提出的，目的是为量子力学提供一个合适的数学框架。共形场论是描述凝聚态物理中临界现象的理论，在弦理论中也占有重要地位。算子代数和共形场论之间的显著相互作用导致了许多有趣的数学问题。 本研究的目的是找到解决一些重要的数学问题，表面在这种情况下，有广泛的应用。

The PI will study interactions between operator algebras and conformal field theories which have proved to be very fruitful lately. The main emphasis of this research is placed on the study of certain representation theory questions such as Kac-Wakimoto conjecture, orbifolds and boundary states in conformal field theories using operator algebraic techniques. The applications of these operator algebraic techniques will lead to proofs of representation theory questions and 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 in condensed matter physics, and it also plays an important role in string theory. The remarkable interactions between operator algebras and conformal field theory has led to many interesting mathematical issues. The aim of this research is to find solutions to some of the important mathematical issues that surface in this context which have a wide range of applications.