Vertex algebras and geometry

手性微分算子的代数，这个项目的中心概念，在这门课上，是由Schechtman， Vaintrob和主要研究者在大约10年前介绍的。以下是该项目涉及的主要主题列表：光滑代数变体上渐近手性微分算子的Gerbes。2. 仿射w代数的渐近手性微分算子及局部化。w -代数和奇点理论。3. 奇异仿射代数变种上的渐近手性微分算子。半无限感应函子与弦理论。本课题属于数学特别是代数几何部分与现代量子场论的交叉领域。经典力学是由泊松代数等代数结构充分描述的，量子化通常在几何表示理论中得到满意的反映。通往领域的通道极大地改变了景观，特别是导致了诸如顶点泊松代数和顶点代数等现代但仍然知之甚少的概念。

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.