Gromov-Witten不变量及其相关的理论是近20年来数学领域中最热门的前沿课题之一。本项目将主要研究高亏格Gromov-Witten不变量和Virasoro猜想。众所周知，Virasoro猜想是Gromov-Witten理论里最基本的问题之一。到目前为止，大家对非半单型的Virasoro猜想知道的结果还很少。在本项目中，我们希望通过研究代数曲线模空间上的Pixton关系式推导出更多的高亏格Gromov-Witten不变量的万有方程，然后结合大相空间量子乘积的性质得到高亏格Virasoro猜想的一些结果。

In the recent 20 years, Gromov-Witten theory has become one of the most important topics in mathematics. In this program, we focus on the higher genus Virasoro conjecture of Gromov-Witten invariants. It is well known that Virasoro conjecture is one of the most basic problems in Gromov-Witten theory. So far, very little is known about non-semisimple Virasoro conjecture. In this project, we hope to obtain more higher genus universal equations of Gromov-Witten invariants via Pixton’s relations on the moduli space of curves, and then prove the higher genus Virasoro conjecture in some cases.