在过去的三十年里，由于与物理的量子场论的结合，数学取得了迅猛的发展， Gromov-Witten理论作为发展趋势中的一个重要分支已经成为当今国际上一个非常热门的方向。该方向涉及的研究方法及应用非常广泛，包括：理论物理中的场论及弦理论、代数几何、辛拓扑与可积系统等。本项目集中研究双有理辛几何、FJRW理论与镜像对称、规范线性σ-模型、Gamma猜测、量子K-理论等。项目组成员在上述领域已经取得了许多重要成果，积累了丰富的研究经验，项目组希望通过本项目的实施完成若干标志性研究成果，提高我国在该领域的整体研究水平。

Over the past thirty years, combining with quantum field theory in Physics, Mathematics developped rapidly. Gromov-Witten theory has become an important branch of Mathematics in those development and a very popular research field . Gromov-Witten theory also involved in a lot of research methods and applications including field theory and string theory from theoretical Physics, algebraic geometry, symplectic topology, integrable systems, and so on. This project will studied birational symplectic geometry, FJRW theory and mirror symmetry, gauged linear σ- model, Gamma conjectures, quantum K-theory,etc. The experts in the program group have made many important progress in this field, and have obtained a lot of research experience. The research team of this program hopes to obtain some remarkable results and improve the research situation in this field with the support of this program.