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.

小行星9622961 这项拨款支持Y教授的研究。黄致力于研究顶点算子理论和共形场论中的各种问题.他希望研究高属共形场理论，特别是它们的应用几何和拓扑。他还希望研究与Virasoro代数，sigma模型和怪物零星群的几何结构有关的几何结构。 这是一项从代数领域开始的研究，但超越了代数领域，涉及数论和理论物理。 这些联系的原因是，代数可以被看作是对抽象对称性的研究。因此，代数在物理和化学领域有直接的应用。特别是现代物理学中的规范场理论广泛地使用了这一领域的代数，本项目将详细研究其中的一些联系。还有编码理论和跨通信线路的数据传输。