Studies on Floer thoery, theory of holomorphic curves and symplectic structures, contact structures

辛结构是在理解哈密顿运动方程时出现的一种几何结构。近年来，辛结构的几何研究有了深刻的发展。特别是，结合镜面对称性的数学研究，辛几何引起了许多研究者的关注。这位研究者一直致力于Floer理论及其应用的研究，Floer理论在辛几何中扮演着重要的角色。在本研究项目中，我们对环形流形中拉格朗日环面纤维的Floer理论进行了具体的研究，得到了许多有趣的结果。

Symplectic structure is a geometric structure, which appeared in the understanding of Hamilton's equation of motion. In recent years, there has been profound development in the geometric study of symplectic structures. In particular, combined with the mathematical study on mirror symmetry, symplectic geometryattracts attentions from many researchers. The investigator has been working on Floer theory, which plays a significant role in symplectic geometry, and its applications. In this research project, we studied Floer theory for Lagrangian torus fibers in toric manifold in a concrete way and obtained various interesting results.