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.

二维共形场论起源于凝聚态物理学和弦论，目前正在数学上进行公式化、构造和研究。它现在是一个深刻的，丰富的和美丽的数学理论，并已导致新的想法，令人惊讶的结果和解决许多数学和物理问题。另一方面，当张量范畴的语言被用作一个统一的概念时，数学和物理学不同领域的各种最新发展可以被认为是相关的。一个例子是模张量范畴，它自然出现在共形场论的研究中，也出现在其他相关的代数和解析结构中。进一步研究共形场论与张量范畴之间的联系，将有助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的热点。人们相信，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，如果构建的话，计算机运行速度比我们现在拥有的计算机快得多。该奖项为数学家和物理学家提供支持，包括研究生，初级教师，妇女和代表性不足的少数群体成员，在美国参加2011年6月14日至6月18日在北京国际数学研究中心举行的“共形场论和张量范畴”研讨会。本次研讨会的目的是汇集美国，中国和其他国家的共形场论，张量范畴和相关主题的研究人员，讨论新成果，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使大量的数学成果和概念，准备使用访问理论物理界的更大一部分，并找到这些结果的新应用。据信，美国、中国和其他国家的数学家和物理学家都可以从交流他们的成果以及发起新的合作和研究项目中受益匪浅。