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

9622961 黄 此项资助支持黄教授研究顶点算子理论和共形场理论中的各种问题。他希望研究更高属的共形场论，特别是它们在几何和拓扑中的应用。他还希望研究与 Virasoro 代数、sigma 模型以及怪物零星群几何相关的几何构造。 这项研究始于代数领域，但超越了代数领域，涉及数论和理论物理。 存在这些联系的原因是代数可以被视为抽象的对称性研究。因此，代数可以直接应用于物理和化学领域。特别是现代物理学中的规范场理论广泛地使用了代数的这一领域，本项目将详细研究其中的一些联系。它还与编码理论和跨通信线路的数据传输有关。

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.