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

9622961这笔助学金支持黄永元教授研究顶点算符理论和共形场理论中的各种问题。他希望研究高亏格共形场理论，特别是它们在几何学和拓扑学中的应用。他还希望研究与Virasoro代数、西格玛模型和怪兽零星群几何有关的几何结构。这项研究始于代数领域，但超越了代数领域，触及了数论和理论物理。之所以有这些联系，是因为代数可以被认为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，这个项目将详细研究其中的一些联系。此外，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.