Workshop on Operator Algebras: Subfactors, K-Theory and Conformal Field Theory

冯·诺伊曼代数的研究最初是由默里和冯·诺伊曼研究的，目的是建立量子力学的数学严谨公式，随着沃恩·琼斯在20世纪80年代早期发起的子因子研究，冯·诺伊曼代数的研究得到了重大推动。子因子理论迅速与统计力学中的连杆不变量和三流形不变量、量子群和精确可解模型联系起来，加强了与物理学的联系。随后，代数、拓扑和共形量子场论（CFT）的深入应用和联系被发现，近年来在这些应用中取得了令人印象深刻的进展。自由概率和平面代数技术相结合，不仅可以构造子因子，而且可以导出统计力学环模型的矩阵模型计算。本次研讨会的重点是塑造算子代数的未来研究方向，汇集了来自子因子理论，k理论和CFT等不同学科的专家，他们将通过讲座和分组会议的参与来考虑解决已确定问题的方法。研讨会的主题包括：-手性CFTS的不同形式（局部共形网，顶点算子代数，Segal框架）之间的联系。-重建程序-再现给定模张量范畴的手性CFT的实现。- C*-代数上的量子对称性。-更高的等变扭曲作为等变堕落束。-冯诺依曼相对熵在CFT，子因子和数学物理之间的联系。研讨会将把刚开始从事研究工作的研究人员与在发现冯·诺伊曼代数的应用方面发挥了重要作用的专家聚集在一起，包括琼斯和沃库列斯库，他们已经同意发言。冯诺依曼代数、子因子、k理论和CFT在过去对群表示、代数拓扑和整个理论物理的研究产生了巨大的影响。在未来，量子理论正迅速成为日常技术的基本组成部分，算子代数的应用正在扩大，并有望为新一代开发新的应用。

Research in von Neumann algebras, originally studied by Murray and von Neumann in order to set up a mathematically rigorous formulation of quantum mechanics, received a major boost with the study of subfactors initiated by Vaughan Jones in the early 1980's. Subfactor theory rapidly led to connections with link and 3-manifold invariants, quantum groups and exactly solvable models in statistical mechanics, reinforcing the connections with physics. Subsequently deep applications and connections have been uncovered with algebraic, topological and conformal quantum field theory (CFT), with impressive progress in recent years in these applications. Free probability and planar algebra techniques have been combined to not only construct subfactors but derive matrix model computations in loop models of statistical mechanics.The focus of this workshop is on shaping the future research directions in operator algebras, bringing together experts from such diverse disciplines as subfactor theory, K-theory and CFT, who will consider solutions to identified problems through a combination of lectures and participative sessions of breakout groups. The topics of the workshop include:- The connections between the different formulations of chiral CFTS (local conformal nets, vertex operator algebras, Segal framework).- The reconstruction programme - realisation of a chiral CFT which reproduces a given modular tensor category.- Quantum symmetries on C*-algebras.- Higher equivariant twists as equivariant Fell bundles.- Connections between von Neumann relative entropy in CFT, subfactors, and mathematical physics.The workshop will bring together researchers at the beginning of their careers with experts who were instrumental in finding applications of von Neumann algebras, including Jones and Voiculescu who have already agreed to speak. Von Neumann algebras, subfactors, K-theory and CFT have had a huge influence on the study of group representations, algebraic topology and across theoretical physics in the past. In a future in which quantum theory is rapidly becoming a fundamental part of everyday technology, the applications of operator algebras is expanding and can be expected to develop new applications for a new generation.