Integrated MSc-PhD Program

SYLLABUS

KSM3E08: Advanced Complex Analysis

Automorphisms of Complex plane and Upper half plane, Analytic continuation, meromorphic continuation along a path, monodromy theorem, Conformal Equivalence for Simply Connected Regions, Conformal Equivalence for Finitely Connected Regions, Analytic Covering Maps, De Branges’s Proof of the Bieberbach Conjecture, Hardy Spaces on the Disk, Potential Theory in the Plane.

Suggested texts:

1. 1. 1. 1. 1. 1. Functions of One Complex Variable II, Conway John B.
               2. Function theory on planar domains, a second course in complex analysis – D. Fisher
               3. Geometric Function Theory Explorations in Complex Analysis – Krantz
               4. Potential Theory – Thomas Ransford