This award will provide support for a mathematical conference to be held at the University of Arizona in January 1989. The purpose of this meeting is to bring together experts in the field of complex analysis to present and discuss ways in which computers are affecting research in this field. The conference will be international in scope combining both theoreticians and computational experts. The need for this gathering has arisen, as in many other areas of mathematics, because of the sharp impact computing has made on attitudes of researchers and their approaches to solving long-standing problems. Examples of phenomena in complex analysis which could not be analyzed by hand have been worked out. New insights, conjectures and, eventually, new theorems have resulted. In addition, computers have created a demand for new methods which would have been of no use in precomputer days. Intense activity in numerous locations has led to research aimed at solving similar problems from different computational points of view. This is particularly noticeable in the area of conformal mapping where improved techniques lead to immediate application in grid approximations to problems in partial differential equations. It is vital that groups such as these be brought together to compare their accomplishments and to introduce others to computation as a valuable tool which can make important contributions to their fundamental research.
