8.17-8.19【张俊升】An introduction to compact and complete non-compact Calabi-Yau manifolds I, II, III

发布时间:2023-08-08来源:几何与物理研究中心中文网页浏览次数:143

报告人:张俊升(加州大学伯克利分校)

时间:2023年8月17、18、19日09:00-11:00

地点:二教2103


摘要Lecture 1: An introduction to compact Calabi-Yau manifolds and related problems

We will talk about Yau’s solution to Calabi’s conjecture, which concerns canonical metrics on Kahler manifolds. It reduces to the solvabilty of some complex Monge-Ampere equations and we will focus on a priori estimate, which includes C^0, C^2, C^{2,\alpha} estimates.

 

Lecture 2:  Asymptotic conical Calabi-Yau manifolds

We will talk about asymptotic conical Calabi-Yau manifolds which form an important class of complete (non-compact) Calabi-Yau manifolds. We will discuss Tian-Yau’s construction and the later development of Goto, Van Coevering and Conlon-Hein.


Lecture 3: A classification for Calabi-Yau manifolds asymptotic to cones

We will discuss a recent result proved by Song Sun and myself. Combining this result with other results in the literature, a classification for Calabi-Yau manifolds with Euclidean volume growth and quadratic curvature decay is given. For the proof, we need Hormander’s L^2-method, Tian-Yau’s construction and Donaldson-Sun’s theory.