Complex Analysis 2, Spring 2019
Tuesday 12-13, Shenkar 204
Thursday 13-15, Multi-disciplinary Center 315
Course outline
- Normal families of meromorphic functions: Marty's theorem, Zalcman's lemma.
- Montel's theorem and the proof of Picard's big and small theorems.
- The Dirichlet problem: harmonic functions, Green's function, Perron's method and the Riemann mapping theorem.
- Riemann surfaces: definitions, examples and basic properties; analytic continuation and monodromy, Green's function; the uniformazation theorem; covering surfaces and a conceptual proof of Picard's theorems.
- Introduction to complex dynamics.
Further reading
- Complex Analysis (3rd edition), Ahlfors.
- Complex Analysis, Gamelin.
- A primer on Riemann Surfaces, Beardon.
- A course in complex analysis and Riemann Surfaces, Schlag.
- Conformal Invariants: Topics in Geometric Function Theory, Ahlfors.
Final grade
The final grade will be based on solutions to homework problems and final take-home exam.
Homework