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

辛结构是在对汉密尔顿运动方程的理解中出现的一种几何结构。 近年来，辛结构的几何研究有了很大的发展。 特别是与镜像对称的数学研究相结合，辛几何引起了许多研究者的关注。 研究人员一直致力于Floer理论，它在辛几何及其应用中发挥着重要作用。 在本研究项目中，我们具体研究了复曲面流形中拉格朗日环面纤维的Floer理论，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.