Complex Analysis and Complex Geometry, Spring 2025

I was the teaching assistant for Professor Huijun Fan’s Spring 2025 course on complex analysis and complex geometry, and delivered the following recitation lectures.

Part I. The Riemann mapping theorem and uniformization

1. Rectifiable curves.
2. Differential forms and differential graded algebras.
3. Stokes’ formula, with applications.
4. The Riemann mapping theorem.
5. The Riemann mapping theorem; the Carathéodory–Osgood theorem; Riemann mappings of polygons.
6. Picard’s little and big theorems; the modular function as the universal cover of $\mathbb{P}^1$ minus three points.

Part II. Conformal and quasi-conformal mappings

1. Conformal maps.
2. Conformal invariants.
3. Quasi-conformal maps.
4. Existence of solutions to the Beltrami equation for a Beltrami coefficient of compact support and norm less than one.