Representation Theory and Quantum Field Theory

9970499本文主要研究光滑流形上顶点代数层的性质，这是Schechhtman，Vaintrob和作者在最近的工作中提出的. 这种研究的最终目的是对相应的上同调顶点代数及其模进行分类。 这应该在量子上同调和镜像对称中找到有趣的应用。顶点代数理论是用于解释共形场论的数学工具。 顶点代数的上述层被认为可以解释拓扑场论中的一些最新发展。 这条研究路线已经产生了某些对数学本身有价值的结果。

9970499The present proposal is focused on the study of sheaves of vertex algebras over smooth manifolds introduced in a recent work by Schechtman, Vaintrob and the author. The ultimate goal of such a study is the classification of the corresponding cohomology vertex algebras and their modules. This should find interesting applications in quantum cohomology and mirror symmetry.The theory of vertex algebras is a mathematical tool intended for the explanation of conformal field theory. The above-mentioned sheaves of vertex algebras are supposed to explain some recent developments in topological field theory. This line of research has already produced certain results valuable for mathematics itself.