Vertex algebras and geometry

顶点代数和几何

• 批准号: 1101078
• 负责人: Feodor Malikov
• 金额: $ 18.08万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-06-01 至 2020-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1101078&HistoricalAwards=false
• 关键词: Vertex; algebras; geometry

Algebras of chiral differential operators, a concept around which this project is centered, are in this class and were introduced by Schechtman, Vaintrob, and the principal investigator some 10 years ago. Here is the list of the main topics addressed in this project: 1. Gerbes of asymptotic chiral differential operators on smooth algebraic varieties. 2. Asymptotic chiral differential operators and localization of affine W-algebras. W-algebras and singularity theory. 3. Asymptotic chiral differential operators on singular affine algebraic varieties. Semi-infinite induction functor and string theory.The present project belongs in the interface of mathematics, especially its algebro-geometric part, and modern quantum field theory. Classical mechanics is adequately described by such algebraic structures as Poisson algebras, quantization is usually satisfactorily reflected in geometric representation theory. The passage to fields drastically changes the landscape and, in particular, leads to such modern and still poorly understood concepts as a vertex Poisson algebra and a vertex algebra.

手征微分算子的代数是本项目的核心概念，属于这一类，大约10年前由Scheck htman、Vaintrob和主要研究人员引入。本课题的主要研究内容如下：1.光滑代数簇上渐近手征微分算子的萌芽。2.渐近手征微分算子与仿射W-代数的局部化W-代数与奇点理论。3.奇异仿射代数簇上的渐近手征微分算子。半无限感应函子和弦理论。本项目属于数学，特别是它的代数几何部分，和现代量子场论的接口。经典力学可以用Poisson代数这样的代数结构来描述，量子化通常很好地反映在几何表示理论中。通向田野的这段旅程极大地改变了地貌，特别是导致了现代的、仍然鲜为人知的概念，如顶点泊松代数和顶点代数。