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.

二维共形场论出现在凝聚态物理和弦理论中，并且正在数学上被公式化、构建和研究。它现在已经成为一种深刻、丰富和美丽的数学理论，并已经为数学和物理学中的许多数学问题带来了新的思想、令人惊讶的结果和解决方案。另一方面，当张量范畴的语言被用作统一概念时，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。一个例子是模张量类别，它自然出现在共形场论以及其他相关代数和解析结构的研究中。进一步研究共形场论与张量范畴的联系将有利于共形场论和张量范畴理论的发展。二维共形场论和张量范畴是近年来数学家和物理学家研究热点的数学理论。人们认为，在自然界和实验室中观察到的许多重要现象，如临界现象、量子霍尔效应、无序现象等，都可以用这些理论来描述。更重要的是，对这些理论的深入理解可能会导致新技术的发展，例如，为人们所说的量子计算机设计芯片的新技术，如果建成的话，计算机的运行速度将比我们现在的计算机快得多。现在有。该奖项为美国的数学家和物理学家提供支持，包括研究生、初级教师、女性和代表性不足的少数群体成员，参加 2011 年 6 月 14 日至 6 月 18 日举行的“共形场论和张量类别”研讨会，在北京国际数学研究中心。本次研讨会的目的是汇集美国、中国和其他国家研究共形场论、张量类别和相关主题的研究人员，讨论新成果、交流想法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让大量的数学结果和概念可供理论物理界的大部分人使用，并找到这些结果的新应用。相信美国、中国和其他国家的数学家和物理学家都可以通过交流他们的成果以及启动新的合作和研究项目而受益匪浅。