In this program
- Riemann surfaces: definitions and examples
- Uniformization theorem (statement)
- Divisors and line bundles
- Sheaves (introduction)
- Hodge theory on Riemann surfaces (optional)
- Nevanlinna theory (optional capstone)
Riemann surfaces and advanced topics
Riemann surfaces: definitions and examples
Complex analysis · Theoretical / proof-based
Topic
Riemann surfaces: definitions and examples
Graduate Complex Analysis — scope drawn from open graduate complex analysis texts and typical US graduate complex analysis syllabi.