U.S.-Australia Planning Visit: Automorphisms of Cauchy-Riemann (CR) Manifolds

0805934Dwilewicz该奖项支持一次计划访问，使密苏里大学罗曼·德威维奇教授能够与阿德莱德南澳大利亚大学的弗拉基米尔教授以及澳大利亚阿米代尔新英格兰大学的格德·施马尔茨教授和亚当·哈里斯教授会面。这次访问将有助于在柯西-黎曼(CR)流形的自同构领域制定一项详细的国际合作研究和教育计划。拟议的活动结合了复分析、微分几何和代数几何，特别是环境复流形中实子流形的几何以及满足切向CR方程的相应函数类。这一研究领域是复数分析和几个复变量研究的中心。这项研究将考虑高余维CR流形及其在复流形中域边界中的作用。密苏里大学罗拉分校和澳大利亚大学之间的利益有足够的重叠，表明它们可以成功地开展拟议的活动，这种互动将使双方受益。美国将在CR流形的局部和全局几何、CR函数的局部和全局逼近和扩展、管形流形和环面变种方面提供专业知识。澳大利亚人是CR流形的范式、CR流形的自同构群及其相关领域的世界级专家。在计划访问之后，德威维奇教授将提出一个研究项目，其中将包括美国研究生的参与。这一机会将为他们提供宝贵的全球研究经验。根据他们的研究经验，预计这些学生在整个职业生涯中可能会与他们的澳大利亚同事保持联系。

0805934DwilewiczThis 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.