9313042 Range Professor John E. Fornaess, a leading international expert in the area of multidimensional complex analysis, will present a series of ten lectures, centering around the behavior of classes of holomorphic self-maps of complex n- dimensional Euclidean spaces and projective spaces. Just as in the one dimensional case - widely known through stunning computer generated visualisations - iteration of such maps in higher dimensions reveals surprising phenomena, and new properties of dynamical systems which need to be understood. While some of the work in dimension two goes back to classical work of Fatou and Bieberbach in the 1920's (Fatou, together with Julia, is one of the pioneers of complex dynamics in dimension one), most of the topics covered in Fornaess' lectures are based on quite recent work. The field is the subject of many current investigations, and there are many open problems. The lectures are intended to make this research area accessible to non-experts in multidimensional complex analysis, and they should help mathematicians new to this field to gain a deeper understanding of the major problems and current directions of research in this new and rapidly expanding research area. The conference will take place June 13 to June 18, 1994, on the campus of the University of Albany, State University of New York. Albany is the center of the Capital District in Upstate New York, a cast region which includes among its many educational institutions the University of Albany, Rensselaer Polytechnic Institute, Union College, Skidmore College and Siena College. Multidimensional complex analysis is an active area of research at the University of Albany, and many experts in classical function theory, ergodic theory and (real) dynamical systems work in the region. A special effort will be made to attract interested participants from neighboring institutions, who may want to enter this research field. It is hoped that this series of lectures will help to build new interactions between mathematicians from the different institutions in the region, and stimulate new research efforts in multidimensional complex analysis in the region.
