This award supports a planning visit to enable Professor Roman Dwilewicz at the University of Missouri in Rolla to meet with Professor Vladimir at the University of South Australia in Adelaide and Professors Gerd Schmalz and Adam Harris at the University of New England in Armidale, Australia. The visit will help develop a detailed international collaborative research and education plan in the area of automorphisms of Cauchy-Riemann (CR) manifolds. The proposed activity combines Complex Analysis, Differential Geometry and Algebraic Geometry, in particular, geometry of real submanifolds in an ambient complex manifold and the corresponding class of functions that satisfy the tangential CR equations. The area of research is central to the study of Complex Analysis and Several Complex Variables. The research will consider the higher codimensional CR manifolds and their role in the boundary of domains in complex manifolds.
There is sufficient overlap of interests between the University of Missouri at Rolla and the Australian Universities to indicate that they can successfully pursue the activities proposed and that the interaction will benefit both sides. The U.S. will contribute expertise in the area of local and global geometry of CR manifolds, local and global approximation and extension of CR functions, tubular manifolds and toric varieties. The Australians are world class experts in normal forms of CR manifolds, groups of automorphisms of CR manifolds and related fields. Following the planning visit, Professor Dwilewicz will propose a research project that will include the participation of U.S. graduate students. This opportunity will provide them a valuable global research experience. Based on their research experience, it is anticipated that the students will likely maintain connections with their Australian colleagues throughout their careers.
