Reporter: Junsheng Zhang (UC-Berkeley)
Time: 09:00-11:00, Aug 17-19, 2023
Place: Room2103, the Second Teaching Building
Abstract: 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.
