时间：2026年3月30日（星期一）14:00-17:00，4月2日（星期四）9:00-12:00，14:00-17:00
地点：E14-416
主讲人：Kuang-Ru Wu, National Central University
讲座主题：Positivity of holomorphic vector bundles in complex geometry
讲座摘要：Positivity properties of holomorphic vector bundles form a central theme in complex and algebraic geometry. A key challenge is to construct Hermitian metrics with positive curvature (in the sense of Griffiths, Nakano, or related notions) on such bundles. The main goal of this mini-course is to present modern techniques for constructing positively curved metrics on vector bundles, with a focus on direct image bundles.
For the first two lectures, we will prove Berndtsson's theorem on positivity of direct image bundles and discuss its applications. In the case of trivial fibration, this theorem has applications to the study of the space of Kahler potentials. In the case of nontrivial fibration, this theorem provides a partial result on a conjecture of Griffiths on the positivity of ample bundles.
For the third lecture, we will prove a subharmonic analogue of the Griffiths conjecture, which relies on the recent developments of the Hermitian-Yang-Mills metrics. Finally, we will introduce RC-positivity, and prove a partial result on a conjecture of Xiaokui Yang. Some open problems will be discussed along the way.
Throughout the mini-course, we aim to keep the presentation largely self-contained, assuming only standard background in complex analysis, Kahler geometry, and Hermitian metrics on bundles. Detailed computations and key estimates will be presented step by step.
