Vertex algebras and geometry

代数的手征微分算子，一个概念，围绕这一项目的中心，是在这一类，并介绍了Schechtman，Vaintrob，和主要研究员约10年前。以下是该项目中涉及的主要主题列表：1.光滑代数簇上渐近手征微分算子的Gerbes。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。半无限归纳函子和弦理论。本项目属于数学的接口，特别是它的代数几何部分，和现代量子场论。经典力学可以用泊松代数这样的代数结构来描述，量子化通常在几何表示论中得到满意的反映。通过领域大大改变了景观，特别是导致这样的现代和仍然很难理解的概念，作为一个顶点泊松代数和顶点代数。

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.