Syllabus Math 543

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