International workshop "Conformal field theories and tensor categories".

国际研讨会“共形场论和张量类别”。

• 批准号: 1105279
• 负责人: Yi-Zhi Huang
• 金额: $ 2万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-05-01 至 2012-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1105279&HistoricalAwards=false
• 关键词: International; workshop; Conformal; field; theories

Two-dimensional conformal field theory arose in both condensed matter physics and string theory and is being formulated, constructed and studied mathematically. It is now a deep, rich and beautiful mathematical theory and has already led to new ideas, surprising results and solutions of many mathematical problems in mathematics and physics. On the other hand, various recent developments in different areas of mathematics and physics can be recognized to be related when the language of tensor categories is used as a unifying concept. One example is modular tensor categories which appear naturally in the study of conformal field theories and also in other related algebraic and analytic structures. Further study of the connection between conformal field theories and tensor categories will benefit the developments of both conformal field theory and the theory of tensor categories.Two dimensional conformal field theories and tensor categories are mathematical theories studied intensely in recent years by both mathematicians and physicists. It is believed that many important phenomena observed in nature and in laboratory, such as critical phenomena, quantum Hall effects, disorder phenomena and so on, can be described by these theories. More importantly, a deep understanding of these theories might lead to the development of new technologies, for example, new technology for the design of chips for what people call quantum computers, which, if constructed, are computers running much much faster than the computers we have now. This award provides support for mathematicians and physicists, including graduate students, junior faculty, women and members of underrepresented minority groups, in the United States to attend the workshop ``Conformal field theories and tensor categories'' from June 14 to June 18, 2011, at the Beijing International Center for Mathematical Research in Beijing. The purpose of this workshop is to bring together researchers in the United States, China and other countries working on conformal field theories, tensor categories and related topics to discuss new results, exchange ideas and initiate new collaborations and research projects. In particular, one of the main goals of the workshop is to make a wealth of mathematical results and concepts that are ready to use accessible to a larger part of the theoretical physics community and to find new applications of these results. It is believed that mathematicians and physicists in the United States, China and other countries can all benefit a lot from communicating their results and from initiating new collaborations and research projects.

二维形式的综合场理论在凝聚的物理和弦理论中都出现，并且正在数学上进行，构造和研究。现在，这是一个深厚，丰富和美丽的数学理论，已经导致了新的想法，令人惊讶的结果以及在数学和物理学中许多数学问题的解决方案。另一方面，当使用张量类别的语言用作统一概念时，可以认为数学和物理不同领域的各种最新发展可以被认为是相关的。一个例子是模块化张量类别，这些类别自然出现在保形场理论研究以及其他相关代数和分析结构中。对保形场理论与张量类别之间的联系的进一步研究将使保形场理论和张量类别的理论都受益。近年来，数学家和物理学家都深入研究了两种维度的结构化理论和张量。据认为，这些理论可以描述许多在自然界和实验室中观察到的许多重要现象，例如关键现象，量子霍尔效应，无序现象等。更重要的是，对这些理论的深刻理解可能会导致新技术的开发，例如，为人们称为量子计算机设计芯片的新技术，如果构建，计算机的运行速度比我们现在拥有的计算机要快得多。该奖项为数学家和物理学家提供了支持，包括研究生，初级教职员工，妇女和代表性不足的少数群体成员，在2011年6月14日至6月18日在北京国际北京国际数学研究中心，参加了``共同田野理论和张量类别''。该研讨会的目的是将美国，中国和其他从事保形领域理论，张量类别和相关主题的研究人员汇集在一起​​，讨论新的结果，交流思想并启动新的合作和研究项目。特别是，研讨会的主要目标之一是制定大量的数学结果和概念，这些成果和概念准备使用可用于理论物理社区的大部分，并找到这些结果的新应用。人们认为，美国，中国和其他国家的数学家和物理学家都可以从传达结果以及启动新的合作和研究项目中受益匪浅。