Mathematical Sciences: Finite Groups & the Theory of Orbifolds

9401272梅森这个奖项是关于有理奥比诺尔德理论的，作为顶点算子代数及其表示的更广泛且目前非常活跃的领域的一部分。它与二维共形场理论密切相关。主要研究人员将研究配分函数的模不变性、扭曲扇形的构造以及更高亏格的一般现象。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下发挥作用。共形场理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。保形场理论除了在物理学中具有重要意义外，其优美而丰富的数学结构也引起了许多数学家的兴趣。在共形场理论的研究中，揭示了无穷维李代数和群的表示、Riemann曲面和代数曲线、Monster零星群、模函数和模形式、椭圆亏格和纽结理论等数学分支之间的新关系。

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.