## Seminar:

Spring 2010, Thursdays, Milner 216, 4:00-4:50 PM

Date: March 4

"  D-bar methods in Complex Analysis "
Prof. Emil Straube

Abstract

Holomorphic functions of a complex variable $z$ are (among other things) solutions of the homogeneous Cauchy-Riemann equation $\partial f/ \partial\overline{z} = 0$. In this talk, I will illustrate the power of this point of view. I will first solve the \emph{in}homogeneous equation on a planar domain. This solution yields a quick and elegant proof of the classical Mittag-Leffler theorem. The last part of the talk will examine new phenomena that arise in dimension two (or more).