Mathematical Sciences: Vertex Operators Algebras, Conformal Field Theories, and Geometry

数学科学：顶点算子代数、共形场论和几何

• 批准号: 9622961
• 负责人: Yi-Zhi Huang
• 金额: $ 6.21万
• 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: 1996
• 资助国家: 美国
• 起止时间: 1996-08-15 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622961&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Vertex; Operators; Algebras

9622961 Huang This grant supports the research of Professor Y. Huang to work on various problems in the theory of vertex operators and conformal field theory. He wishes to study higher-genus conformal field theories, especially their applications to geometry and topology. He also hopes to study geometric constructions related to Virasoro algebras, sigma models, and the geometry of the monster sporadic group. This is research that starts out in the field of algebra but moves beyond that to touch both number theory and theoretical physics. The reasons for these connections are that algebra can be though of as the study of symmetry in the abstract. As such algebra has direct applications to areas of physics and chemistry. In particular the modern theory of gauge fields in physics uses this area of algebra extensively and this project will study some of these connections at length. There are also connections to coding theory and the transmission of data across communication lines.

9622961黄这个赠款支持Y. Huang教授的研究，以解决顶点操作员理论和保形领域理论中的各种问题。他希望研究更高的保形野外理论，尤其是它们在几何和拓扑上的应用。他还希望研究与Virasoro代数，Sigma模型和Monster零星组的几何形状有关的几何结构。 这是从代数领域开始的研究，但超越了触摸数字理论和理论物理学。 这些连接的原因是代数可以作为抽象的对称性研究。因此，这种代数直接应用于物理和化学领域。特别是，物理学量规场的现代理论广泛使用了代数的这一区域，该项目将详细研究其中一些连接。与编码理论以及跨通信线的数据传输也有连接。