Complex Analysis beyond One Dimension

Mehmet Celik, University of Arkansas at Fort Smith
Complex Analysis beyond One Dimension
October 8, 2009

Abstract: The study of functions defined on multidimensional complex space is called the theory of several complex variables. Classical complex analysis is the study of functions defined on one dimensional complex space. The main object of study in both theories is complex analytic functions. Some parts of the theory of analytic functions, such as the maximum principle, normal limit of nowhere-zero analytic functions, and Cauchy's estimates for derivatives, are essentially the same in all dimensions. The most interesting parts of the multidimensional complex theory are the features that differ from the one dimensional theory. At the beginning of the presentation, we will mention some differences between these two theories from different points of view. Then, we will focus on one particular difference and explore the world of complex analysis beyond one dimension. The talk is accessible to any graduate students in mathematics.