Mathematical Sciences: Finite Groups & the Theory of Orbifolds

数学科学：有限群

• 批准号: 9401272
• 负责人: Geoffrey Mason
• 金额: $ 6万
• 依托单位: University of California-Santa Cruz
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401272&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Finite; Groups; &amp

9401272 Mason This award is concerned with the theory of rational orbifolds as part of the broader, and currently very active area, of vertex operator algebras and their representations. It is closely associated to 2-dimensional conformal field theory. The principal investigator will examine questions of modular-invariance of partition functions, the construction of twisted sectors, and the general phenomena of higher genus orbifolds. Methods include ideas from vertex operator algebra theory, modular forms and group theory, all of which play a role in the so-called Moonshine. Conformal field theory is an important physical theory describing both two-dimensional critical phenomena in condensed matter physics and classical motions of strings in string theory. Besides its importance in physics, the beautiful and rich mathematical structure of conformal field theory also has interested many mathematicians. New relations between different branches of mathematics, such as representations of infinite-dimensional Lie algebras and groups, Riemann surfaces and algebraic curves, the Monster sporadic group, modular functions and modular forms, elliptic genera, and knot theory, is revealed in the study of conformal field theory.

9401272梅森：这个奖项是关于有理轨道的理论，它是目前非常活跃的更广泛的顶点算子代数及其表示领域的一部分。它与二维共形场论密切相关。主要研究者将研究配分函数的模不变性问题，扭曲扇区的构造，以及高属轨道的一般现象。方法包括顶点算子代数理论、模形式和群论的思想，所有这些都在所谓的月光中发挥作用。共形场论是描述凝聚态物理中的二维临界现象和弦理论中弦的经典运动的重要物理理论。除了在物理学上的重要性外，共形场论美丽而丰富的数学结构也引起了许多数学家的兴趣。在共形场论的研究中，揭示了无限维李代数与群的表示、黎曼曲面与代数曲线、怪物散群、模函数与模形式、椭圆属、结论等数学不同分支之间的新关系。