Topics on complex analysis Spring 2022

This topic course will cover the following topics:

1. Complex and differential geometry: Riemannian/Kahler metrics, curvatures, vector bundles
2. basic PDE theory: Schauder estimates, regularity theory for linear equations
3. Metric geometry: Gromov-Hausdorff topology, introductory Cheeger-Colding theory
4. Complex Monge-Ampere equations: proof of Calabi conjecture
5. Hormander’s L^2 estimates for solving d-bar equations: proof of Kodaira embedding theorem, partial C0 estimates, expansion of Bergman kernel

The lecture notes can be found:

Part I

Part II

Part III

Part IV