Operator Algebras and Conformal Field Theories

徐斌PI将研究算子代数和共形域理论之间的相互作用，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利用算子代数方法研究某些表示论问题，如Kac-Wakimoto猜想，共形场论中的轨道折叠和边界态。这些算子代数技巧的应用将导致证明表示论问题和阐明外来子因子，如那些来自共形包含。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，在弦论中也占有重要地位。算子代数与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一些重要的数学问题的解决方案，表面在这种情况下，有广泛的应用。

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.