课程名称： Some aspects related to hyperbolicity problem
课程安排：分两部分，每部分8课时，共计16课时
第二部分： Introduction to non-abelian Hodge theory
主讲人： 孙锐然 (德国美因茨大学)
时间：2021年6月10/17/24， 7月1日下午14:00-16:00.
地点：6月10-24日后主楼1124， 7月1日后主楼1220.
摘要：
Non-abelian Hodge theory was established by the fundamental papers of Hitchin and Simpson, and is developed by many people's works. Just as the classical Hodge theory, it has important applications in complex geometry and algebraic geometry.
In the first talk, we will introduce the notion of Higgs bundles and the famous Hitchin-Simpson correspondence. We also give some application of this theorem. As an important special case, we will talk about the Hodge bundles associated to variation of Hodge structures.
In the second talk, we will explain the fundamental work of Viehweg-Zuo on the hyperbolicity of moduli spaces of polarized manifolds, in which the nice curvature property of Hodge bundles plays a crucial role.
In the third talk, we will talk about the application of non-abelian Hodge theory in the study of linear Shafarevich conjecture. More precisely, we will explain Zuo's work on the Chern hyperbolicity of projective varieties whose fundamental groups admit big linear representations.
In the fourth talk, we will discuss the recent work of Feng Hao on \pi_1-small divisors on quasi-projective varieties. As an application, he also obtains hyperbolicity properties of smooth projective surfaces of general type with infinite fundamental groups. We will explain the idea of his proof.
主讲人简介：孙锐然，本科毕业于西安交通大学。2016年于中国科学技术大学取得硕士学位后，前往德国美因茨大学攻读博士学位，师从左康教授和 Ariyan Javanpeykar。博士论文中证明了极化流形模空间上的皮卡型延拓定理，推广了 Amand borel 关于局部有界对称簇的经典结果。
