The Algebraic Structure of Topological Field Theory

9704320盖茨勒在这个项目中，研究人员将阐明理论物理中某些最新发现背后的代数结构，包括二维拓扑西格玛模型、拓扑引力和格罗莫夫-维腾不变量。特别地，推导了Gromov-Witten不变量的结构理论，并计算了高亏格的Gromov-Witten不变量。在数学术语中，这些不变量与代数几何中的各种计数问题有关。例如，零亏格的Gromov-Witten不变量出现在所谓的镜像对称现象中。Gromov-Witten不变量最初出现在理论物理中--它们描述了拓扑引力与保形场理论模型的耦合。它们在流行的宇宙10维弦模型中扮演着重要的角色。弦理论模型包含六个隐藏维度，它们形成了一个称为Calabi-Yau流形的紧曲空间；Gromov-Witten不变量可用于研究Calabi-Yau流形的各种数学性质。

9704320 Getzler In this project the investigator is to clarify the algebraic structures underlying certain recent discoveries in theoretical physics including the two-dimensional topological sigma model, topological gravity, and Gromov-Witten invariants. In particular, a structure theory for Gromov-Witten invariants is to be derived, and Gromov-Witten invariants of higher genus are to be computed. In mathematical terms, these invariants relate to various enumerative questions in algebraic geometry. For example, Gromov-Witten invariants of genus zero appear in the so called mirror symmetry phenomenon. Gromov-Witten invariants originally arose in theoretical physics - they describe a coupling of topological gravity with a model of conformal field theory. They play an important role in the popular 10-dimensional string model of the universe. The string theory model contains six hidden dimensions which form a tightly curved space known as Calabi-Yau manifold; Gromov-Witten invariants can be used to study various mathematical properties of Calabi-Yau manifolds.