MATH 704 Syllabus
Here is a preliminary list of the topics that I plan to discuss in the course, subject to revision:
- Weierstrass product and factorization theorems
- Jensen's formula and applications
- Blaschke products and their zeros
- Order of an entire function, Hadamard's factorization theorem
- Rational and polynomial approximation
- 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 and Picard
- Geometry in the hyperbolic plane, Ahlfors's version of the Schwarz lemma
- Holomorphic covering and branched covering maps
- The Uniformization theorem
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Math 704