Cornell Math - Math 612 (SP01)

Math 612 — Spring 2001
Complex Analysis

Text: Conway, "Functions of one complex variable," plus additional lecture notes

Prerequisite: Math 611

This is the required graduate course in complex analysis. We will cove standard material in one complex variable theory, including the Riemann mapping theorem, the two Picard theorems and an introduction to Riemann surfaces. In addition, we will do the elements of distribution theory and Fourier transforms, including the Paley-Wiener theorem on the analytic continuation of Fourier transforms of functions of compact support. As an application of complex analysis to PDEs, we will prove the Malgrange-Ehrenpreis theorem on existence of solutions to constant coefficient linear equations.

Students will be expected to do most of the lecturing in the course and will be required to complete a small project exploring some topic in greater depth.