9501517 Ahern The project involves research on several problems related to the automorphism group of n-dimensional complex Euclidean space. For automorphisms of finite period the two main problems are the linearization problem and the related fixed point problem. Another theme treated in this project is the question of describing, in some sense, all one parameter subgroups and the related question of determining which automorphisms have square roots in the sense of composition. This project is a synthesis of complex geometry, algebra and analysis. The project involves understanding the algebraic and fixed point structure of certain transformations on n-dimensional complex space. These transformations are called automorphisms which means that they preserve the shape of the space. In one direction the research asks whether certain of these automorphisms are linear, i.e., preserve linear structure. In another direction one tries to determine whether these automorphisms behave like linear automorphisms in the sense of having fixed points. These automorphisms play an important role in the study of complex manifolds. ***
