US-Austria Workshop: Tensor Categories in Mathematics and Physics

美国-奥地利研讨会：数学和物理中的张量类别

• 批准号: 0406198
• 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: 2004
• 资助国家: 美国
• 起止时间: 2004-06-01 至 2005-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0406198&HistoricalAwards=false
• 关键词: US; Austria; Workshop; Tensor; Categories

0406198HuangVarious recent developments in different areas of mathematics and physics turn out to be related when the language of tensor categories is used as a unifying concept. Tensor categories emerge naturally whenever a mathematical problem needs an efficient treatment of one or several products," or when a problem in theoretical physics requires a concise description of possible couplings. As a consequence, tensor categories provide a natural unifying language for many interesting problems. Using this framework has the additional benefit of unraveling structural parallels and therefore often allows one to apply results and techniques to a given problem that were originally developed in a different context.The PI is a co-organizer of a program, Tensor Categories in Mathematics and Physics, to take place in the spring and early summer of 2004 at the Erwin Schroedinger Institute in Vienna. The purpose of this program to bring together researchers working on different topics in mathematics (such as quantum groups, link invariants, vertex algebras, or subfactors) and physics (such as topological and conformal field theory, string theory, or operator algebraic approaches to quantum theory) in which tensor categories are playing a role, or can be expected to play a role in the future.The contribution from NSF will be primarily used to support graduate students, junior faculty, women and members of underrepresented minority groups in the United States to attend the program. Active participation in such a program will undoubtedly have an important impact on their future careers. The idea of the program is to encourage interaction between mathematicians and mathematical physicists of different backgrounds. In particular, one of the main goals of the program 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. It is clear that mathematicians and physicists can all benefit from communicating results between the various disciplines and from developing a unified language.

0406198Huang 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被证明是相关的。 每当数学问题需要有效处理一个或多个乘积时，或者当理论物理问题需要对可能的耦合进行简明描述时，张量类别就会自然出现。因此，张量类别为许多有趣的问题提供了一种自然的统一语言。使用这个框架还有一个额外的好处，那就是揭示结构上的相似之处，因此通常允许人们将最初在不同背景下开发的结果和技术应用于给定问题。PI 是数学张量类别和数学张量类别项目的共同组织者。物理学，将于 2004 年春季和初夏在维也纳埃尔文·薛定谔研究所举行。该计划的目的是将研究不同数学主题（例如量子群、链接不变量、顶点代数或子因子）的研究人员聚集在一起。 ）和物理学（例如拓扑和共形场论、弦理论或量子理论的算子代数方法），其中张量类别正在发挥作用，或者有望在未来发挥作用。 NSF 的捐款将主要用于支持美国的研究生、初级教员、女性和少数群体成员参加该项目。 积极参与这样的计划无疑会对他们未来的职业生涯产生重要影响。 该计划的想法是鼓励不同背景的数学家和数学物理学家之间的互动。 特别是，该计划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。 显然，数学家和物理学家都可以从不同学科之间交流结果和开发统一语言中受益。