本项目主要研究Teichmüller测地流上的Lyapunov指数和Harder-Narasimhan滤链. 我们将利用Atiyah-Bott,Forni,Möller的工作来建立它们与Hodge丛曲率特征值的积分之间的关系，并结合Eskin-Kontsevich-Zorich关于Lyapunov指数的数值计算以及Eskin-Mirzakhani-Mohammadi，Eskin-Bonatti-Wilkinson证明的Lyapunov指数的连续性，从而对Teichmüller测地流的Lyapunov polygon和Harder-Narasimhan polygon之间可能存在的关系进行深入的研究和探讨，力求在该方面取得令国内外同行关注的一系列具有突破性和原创性的研究结果。

This project mainly studies Lyapunov exponents and Harder-Narasimhan filtrations on Teichmüller geodesic flows. We will discuss the connections between them and the integral of eigenvalues of the Hodge bundle curvature by using Atiyah-Bott, Forni and Möller's works, and combine Eskin-Kontsevich-Zorich's numerical experiments with Eskin-Mirzakhani-Mohammadi, Eskin-Bonatti-Wilkinson's works on the continuity of Lyapunov exponents, thus in-depth study the possible relation between Lyapunov polygon and Harder-Narasimhan polygon on Teichmüller geodesic flows. Finally, we hope to obtain some ground-breaking and original results in this field.