近二十年来，曲线计数理论成为了代数几何、辛几何与数学物理中的重要研究方向，对其在几何手术下的变化行为的研究吸引了数学家与物理学家的注意。在本项目中，我们将研究Gromov-Witten理论与Donaldson-Thomas理论在双有理手术下的变化情况。对于Gromov-Witten理论，我们计划研究量子极小模型猜想，以及量子上同调的半单性在blow-up下的变化。对于Donaldson-Thomas理论，我们期望建立flop公式，这将提供一种理解GW/DT猜测的可能途径。

During the last two decades, curve counting theories have become important in algebraic geometry, symplectic geometry and mathematical physics, and the study of their behavior under geometric surgeries has attracted the attention of both mathematicians and physicists. In this project, we will study the transformation of Gromov-Witten and Donaldson-Thomas theories under birational surgeries. For Gromov-Witten, we plan to study the quantum minimal model conjecture, and the change of simisimplicity of quantum cohomology under blow-ups. For Donaldson-Thomas, we expect to establish flop formulae, which will provide a possible way to understand the conjectural GW/DT correspondence.