几何流及其应用是近几十年来微分几何领域的重要课题。Hamilton引入的Ricci流使人们看到了几何流方法的强大。于是人们自然想到用几何流的方法去研究其他几何结构。对于Kähler流形，可以直接运行Ricci流，即得到Kähler-Ricci流。而对于不满足Kähler条件的non-Kähler几何，直接运行Ricci流并不能保持相应的几何结构。于是从2008年开始，Streets和田刚引入了一系列non-Kähler几何流来研究相应的non-Kähler结构。本项目旨在对这些non-Kähler几何流，特别是辛曲率流和广义Kähler-Ricci流（或pluriclosed流）进行深入研究，从而解决与之相关的若干问题。具体问题涉及以下几个方面：寻找辛曲率流中的单调性泛函，证明pluriclosed流最大存在时间的同调类刻画，构造广义Hermitian曲率流。

Geometric flow and its application is an important subject in the field of differential geometry in these decades. From the Ricci flow introduced by Hamilton, people recognized that the geometric flow method is very powerful. So naturally, people considered to use geometric flow to study other geometric structures. For Kähler manifolds, we can run the Ricci flow directly, which is the Kähler-Ricci flow. While for non-Kähler geometry which Kähler condition doesn't hold, the geometric structure won't preserve if we run the Ricci flow directly. Then since 2008, Streets and Tian introduced a series of non-Kähler geometric flows to study the corresponding non-Kähler structures. This program aims to study these non-Kähler geometric flows, especially for the symplectic curvature flow and the generalized Kähler-Ricci flow (or the pluriclosed flow) in deep, and to solve some relevant problems. The problems involve the following aspects: to find monotone functionals in symplectic curvature flow, to prove the maximal existence time under the description of cohomology and to construct generalized Hermitian curvature flow.