本课题研究Bose-Einstein condensate、 球面上超导Ginzburg-Landau模型及Maxwell-Higgs模型方程解的零点集结构及其动力学行为。这类问题有强烈的物理背景，又与几何发展方程密切相关，是当前偏微分方程及微分几何领域非常活跃的课题。研究这些问题能更好地理解几何与物理的关系。

In this project, we study dynamics and geometric construction of nodal set of solutions for some partial differential equations. We focus on Gross-Pitaevskii equations about Bose-Einstein Condensates, Ginzburg-Landau model for superconductivity on sphere and Maxwell-Higgs model. These problems are very important both in theoretic physics and in differential geometry. The purpose of this project is to promote better understanding of the relation of theoretic physics and geometry.