Math 543. Complex Variables II Instructor Syllabus
This course covers subjects fundamental to current research in complex and geometric analysis. Topics include
- Riemann Surfaces (The Uniformization Theorem and the Monodromy Theorem)
- Hyperbolic Metric in Planar Domains and Applications
- Potential Theory (Dirichlet Problem, Green's Function and Harmonic Measure)
- Quasiconformal Mappings in the Plane
Other topics that may also be included are
- Univalent Functions, Value Distribution Theory, and Complex Dynamics
Textbooks used in past semesters:
- L.V. Ahlfors, Conformal invariants, McGraw–Hill, New York, 1973
- A.F. Beardon, A primer on Riemann surfaces, Cambridge Univ. Press, 1984
- O. Lehto, Univalent functions and Teichmuller spaces, Springer, New York, 1987
- T. Ransford, Potential theory in the complex plane, Cambridge Univ. Press, 1995
June 10, 2010