Advanced Complex Analysis – I
This is the first part of a series of lectures on advanced topics in Complex Analysis. By advanced, we mean topics that are not (or just barely) touched upon in a first course on
Complex Analysis. The theme of the course is to study zeros of analytic (or holomorphic) functions and related theorems. These include the theorems of Hurwitz and Rouche, the
Open Mapping theorem, the Inverse and Implicit Function theorems, applications of those theorems, behaviour at a critical point, analytic branches, constructing Riemann surfaces
for functional inverses,Analytic continuation and Monodromy, Hyperbolic geometry and the Riemann Mapping theorem. For more details, please look at the titles, goals and keywords
for each lecture given below.