This lecture is a gentle introduction to the hyperbolicity of moduli spaces of complex polarized manifolds with semiample canonical bundles, based on previous works by Viehweg-Zuo, the speaker etc. I will also explain the recent work on the hyperbolicity of varieties admitting variation of Hodge structures. The content is planned as follows:

1. Notions of hyperbolicity of complex manifolds and some tools like Nevannlina theory

2. Variation of Hodge structures and Higgs bundles

3. Positivity of direct images

4. Proof of Viehweg-Zuo's conjecture on the hyperbolicity of polarized varieties

5. A generalization of To-Yeung's theorem on the Kobayashi hyperbolicity of polarized varieties of general type

6. Hyperbolicity of moduli of Hodge structures

A basic knowledge of complex geometry should be enough to follow the lecture.

邓亚 研究员，CNRS(法国国家科学研究中心)和Université de Lorraine。

Zoom Meeting ID：849 963 1368  

Password: YMSC