Forstneric will work on (a) the holomorphic automorphism groups of certain complex manifolds, with the emphasis on Stein manifolds with infinite dimensional automorphism groups (such as the complex Euclidean spaces); (b) applications of the above to the construction of proper holomorphic embeddings in Euclidean spaces with low codimension (such as the embedding of open Riemann surfaces in the complex two-dimensional plane); (c) topics in polynomial and rational convexity; (d) topological properties of pseudoconvex domains. The research topics in (a) include the approximation and interpolation of holomorphic mappings (or smooth mappings from real submanifolds) by holomorphic automorphisms, the classification problems for finite holomorphic transformation groups on low dimensional complex Euclidean spaces, existence and classification of (complete) holomorphic flows on low dimensional Euclidean spaces and other related manifolds, dynamical properties of automorphisms, etc. In many natural and social sciences one tries to explain phenomena by choosing a suitable model space (usually such a space is a manifold in mathematical language) such that each point of the space represents certain state of the observed system, and the laws governing the system can be expressed as algebraic or differential conditions (equations or inequalities) on the given space. Global symmetries of these model spaces (automorphisms in our language) often play a very important role in understanding the structure and properties of solutions of the considered problem(s), and they often help simplifying the problem by changing it to certain standard (model) problem for which the solutions are well understood. Often the natural model spaces are complex manifolds (as opposed to the real manifolds), the simplest being the complex Euclidean spaces. Their automorphisms have much more rigidity and are much less understood than their real counterparts. This is our main motivation for studying g lobal automorphisms of model complex manifolds and their applications.
