NSF-CGP Science Fellowship Program: Research in Geometry and Topology

该奖项将支持纽约罗切斯特大学数学系Martin Guest教授与日本东京工业大学数学系matsuo Oka教授的合作研究项目。东京都大学的Yoshihiro Ohnita博士和东京大学的Mikio Furuta博士也将参与该项目。在为期12个月的访问期间，盖斯特教授和他的日本同事将继续他们之前对黎曼曲面到李群的谐波映射空间拓扑结构的联合研究。从传统微分几何和数学物理规范理论的角度来看，这些图都很有趣。研究人员将系统地描述完全交变的奇异性和映射的奇异性。完全交变可以解释为仿射空间或环面空间之间全纯映射的正则纤维。他们将尝试确定在给定映射的同伦下，规则纤维或奇异纤维的拓扑结构是如何变化的。研究结果在高等数学理论以及理论原子物理等物理学的各个领域都有可能得到应用。Guest教授是一位颇有成就的数学家，目前是将变分原理（调和映射）应用于数学物理问题（特别是孤子和规范理论）领域的几位权威之一。奥卡博士是研究环礁植物品种的权威。Ohnita博士擅长微分几何领域，特别是李群和谐波映射，古田博士的专长是Yang-Mills瞬子的模空间。日本在环变、无限维李代数和可积系统领域处于世界领先地位。由于研究人员之前的合作在新的研究方向和出版物方面证明是非常富有成效的，因此预计拟议的项目将提供类似的新的科学机会。该项目由NSF-CGP（全球伙伴关系中心）科学奖学金计划支持。＊＊＊

9303037 Guest This award will support a cooperative research project between Professor Martin Guest, Department of Mathematics, University of Rochester, New York, and Professor Mutsuo Oka, Department of Mathematics, Tokyo Institute of Technology in Japan. Dr. Yoshihiro Ohnita of the Tokyo Metropolitan University and Dr. Mikio Furuta at Tokyo University will also participate in the project. During his twelve- month visit Professor Guest and his Japanese colleagues will continue their previous joint research on the topology of the space of harmonic maps of a Riemann surface into a Lie group. These maps are of interest from the point of view of traditional differential geometry and also from the point of view of gauge theories in mathematical physics. The researchers will study a systematical description of the singularities of complete intersection varieties and singularities of the mappings. A complete intersection variety will be interpreted as the regular fiber of a holomorphic mapping between affine or toric spaces. They will attempt to determine how the topology of regular fiber or singular fibers changes under a homotopy of a given mapping. Results of the research have probable application in advanced mathematics theories as well as various areas of physics such as theoretical atomic physics. Professor Guest is an accomplished mathematician who is currently one of several authorities working in the field of variational principles (harmonic maps) as applied to problems in mathematical physics, specifically solitons and gauge theory. Dr. Oka is an authority on toric varieties. Dr. Ohnita has expertise in the area of differential geometry, especially Lie groups and harmonic maps and Dr. Furuta's specialty is moduli spaces of Yang-Mills instantons. Japan is a world leader in the areas of toric varieties and infinite dimensional Lie algebras and integrable systems. Since the investiga- tor's previous collaboration proved to be very produ ctive in terms of new directions of research as well as in terms of publications it is anticipated that the proposed project will provide similar new scientific opportunities. This project is supported by the NSF-CGP (Center for Global Partnership) Science Fellowship Program. ***