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.