Applications of holomorphic curves in symplectic topology

本文将研究闭全纯曲线不变量和开全纯曲线不变量在辛拓扑中的应用。关键工具将是与量子和辛上同调、花理论及其代数结构相关的不变量。要解决的基本问题包括辛形态群的性质，辛形态在拉格朗日子流形上的作用，以及与代数几何和热带几何以及镜像对称的联系。

This thesis will investigate applications of closed and open holomorphic curve invariants in symplectic topology. The key tools will be invariants related to quantum and symplectic cohomology and to Floer theory, and its algebraic structures. Basic questions to be addressed include properties of symplectomorphism groups, the action of symplectomorphisms on Lagrangian submanifolds, and connections to algebraic and tropical geometry and to mirror symmetry.