9704837 Barrett This project lies in the general area of several complex variables. Among the topics to be pursued are: function theory on the basins of superattracting fixed points of multivariate complex dynamical systems; graph-theoretic methods for analysis of problems on open Riemann surfaces; Seiberg-Witten metrics on Riemann surfaces; boundary behavior of biholomorphic maps in higher dimensions. Research in several complex variables deals with spaces modeled on complex Euclidean space and mappings between them. Complex numbers, originally introduced in the study of polynomial functions, continue to be useful in simplifying and unifying various aspects of more general functions and maps. Moreover, it has found applications in other parts of mathematics and other sciences such as dynamical systems and theoretical physics.
