Complex Analysis and Complex Geometry 2025 Spring

I was the TA of the 2025 Spring Complex Geometry course taught by Huijun Fan.

Part I. Riemann mapping theorem and Riemann uniformaization

(1) Lec-1 Rerectifiable curves,

(2) Lec-2 Differential form and differential graded algebra,

(3) Lec-3 Stoke’s formula with applications,

(4) Lec-4 Riemann mapping theorem,

(5) Lec-5 Riemann mapping theorem, Caratheodory-Osgood theorem, Riemann mapping on polygon,

(6) Lec-6 Little Picard theorem, Big Picard theorem, modular function as universal cover of P1 remove 3 points,

Part II. Theory of conformal mapping, quasi-conformal mapping

(7) Lec-7 Conformal map,

(8) Lec-8 Conformal invariant,

(9) Lec-9 quasi-conformal map,

(10) Lec-10 Existence of solution for Beltrami differential equation when the Beltrami coefficient has compact supp and <1.