Here is a preliminary list of the topics that I plan to discuss in the course, subject to minor revision:
- Weierstrass product and factorization theorems
- Jensen's formula and its applications
- Blaschke products and their zeros
- Rational and polynomial approximation
- Natural boundary, overconvergence and Hadamard's gap theorem
- Analytic continuation, the monodromy theorem
- Distortion theorems for conformal maps
- Length-area inequalities, conformal invariants
- Boundary behavior of conformal maps
- Non-tangential limits, theorems of Fatou and Riesz brothers
- Theorems of Bloch, Picard and Montel
- Holomorphic covering and branched covering maps
- The uniformization theorem
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