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

冯诺依曼代数的研究最初是由Murray和von Neumann研究的，目的是建立一个严格的量子力学数学公式。随着Vaughan Jones在20世纪80年代初的S开创的对子因子的研究，对von Neumann代数的研究得到了极大的推动。子因子理论迅速导致了与统计力学中的链接和3-流形不变量、量子群和精确可解模型的联系，加强了与物理的联系。随后，代数量子场论、拓扑量子场论和共形量子场论的深入应用和联系被揭示，近年来在这些应用方面取得了令人印象深刻的进展。自由概率和平面代数技术的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，汇聚子因子理论、K-理论和CFT等不同学科的专家，他们将通过分组讲座和参与会议来考虑确定问题的解决方案。研讨会的主题包括：-手性cFTS(局部共形网络、顶点算子代数、西格尔框架)不同公式之间的联系。-重建计划-重现给定模张量范畴的手性CFT的实现。-C*-代数上的量子对称。-作为等变Fall丛的更高等变扭曲。-CFT中的冯·诺伊曼相对熵、子因子和数学物理之间的联系。研讨会将把职业生涯初期的研究人员与在发现冯·诺依曼代数的应用方面发挥重要作用的专家聚集在一起，包括已经同意发言的琼斯和沃特库斯库。Von Neumann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。在量子理论正在迅速成为日常技术的基本部分的未来，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.