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

算子代数研讨会：子因子、K 理论和共形场论

• 批准号: EP/V013203/1
• 负责人: Gandalf Lechner
• 金额: $ 2.37万
• 依托单位: CARDIFF UNIVERSITY
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FV013203%2F1
• 关键词: Workshop; Operator; Algebras; Subfactors; Theory

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.

冯·诺依曼代数的研究最初是由默里和冯·诺依曼为了建立量子力学的数学严格公式而进行的，随着沃恩·琼斯在20世纪80年代初发起的子因子研究，冯·诺依曼代数的研究得到了重大的推动。子因子理论迅速导致了与链接和3流形不变量，量子群和统计力学中的精确可解模型的联系，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揭示出来，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，还可以在统计力学的循环模型中导出矩阵模型计算。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讨论的参与性会议相结合的方式，考虑解决已查明的问题的办法。研讨会的主题包括：-手性CFTS（局部共形网，顶点算子代数，Segal框架）的不同配方之间的连接。重建程序-实现再现给定模张量类别的手征CFT。C*-代数上的量子对称性更高的等变扭曲作为等变Fell丛。冯·诺依曼相对熵在CFT，子因子和数学物理之间的联系。研讨会将汇集研究人员在他们的职业生涯开始与专家谁是在寻找冯·诺依曼代数的应用，包括琼斯和Voiculescu谁已经同意发言。冯·诺依曼代数、子因子、K理论和CFT在过去对群表示、代数拓扑和跨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。