本项目将研究曲线计数理论中的Donaldson-Thomas不变量和相对Gromov-Witten不变量。具体而言，我们会发展代数叠的形变到法锥来处理3维广义Donaldson-Thomas不变量，考虑导出叠的4维Donaldson-Thomas不变量，以及通过局部化和quasimap计算相对Gromov-Witten不变量。

In this project, we will study Donaldson-Thomas invariants and Gromov-Witten invariants in curve couting theories. Specifically, we will develop deformation to the normal cone for algebraic stacks to study generalized Donaldson-Thomas invariants for 3 folds, consider DT4 invariants for derived stacks, and calculate Gromov-Witten invariants using localization and quasimap theory.