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.

默里（Murray）和冯·诺伊曼（Von Neumann）最初研究的冯·诺伊曼（Von Neumann）代数的研究是为了建立数学上严格的量子力学表述，并随着沃恩·琼斯（Vaughan Jones）在1980年代初期发起的亚比例的研究得到了重大提升。子因子理论迅速导致与链接和3个manifold不变性，量子组以及统计力学中准确解决模型的联系，从而加强了与物理的联系。随后，深度应用和连接已被代数，拓扑和保形量子场理论（CFT）发现，近年来在这些应用中取得了令人印象深刻的进步。 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突破组。研讨会的主题包括： - 手性CFT的不同配方之间的连接（局部保形网络，顶点操作员代数，Segal框架）。-重建程序 - 手动CFT的实现，实现了给定模块化的类别。 CFT，子因子和数学物理学中的Von Neumann相对熵之间的联系。该研讨会将在职业生涯开始时与专家一起将研究人员汇集在一起​​，这些专家有助于寻找冯·诺伊曼代数的应用，包括琼斯和沃德雷斯库，他们已经已经同意讲话。冯·诺伊曼（Von Neumann）代数，子因素，K理论和CFT对过去的群体表示，代数拓扑以及过去的理论物理学的研究产生了巨大影响。在量子理论迅速成为日常技术基本组成部分的未来中，操作员代数的应用正在扩大，并且可以预期为新一代开发新的应用程序。