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

NSF-CGP 科学奖学金计划：几何和拓扑研究

• 批准号: 9303037
• 负责人: Martin Guest
• 金额: $ 6.67万
• 依托单位: University of Rochester
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-12-15 至 1997-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9303037&HistoricalAwards=false
• 关键词: NSF; CGP; Science; Fellowship; Program

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. ***

9303037嘉宾该奖项将支持纽约罗切斯特大学数学系马丁·盖斯特教授和日本东京工业大学数学系大贺武夫教授之间的合作研究项目。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。在他为期12个月的访问期间，Guest教授和他的日本同事将继续他们先前关于黎曼曲面到Lie群的调和映射空间的拓扑的联合研究。从传统微分几何的观点和数学物理规范理论的观点来看，这些映射都是有趣的。研究人员将系统地描述完全交簇的奇点和映射的奇点。完全交簇将被解释为仿射空间或环面空间之间的全纯映射的正则纤维。他们将试图确定在给定映射的同伦下，规则纤维或奇异纤维的拓扑如何变化。研究结果可能在高等数学理论以及各种物理领域，如理论原子物理中得到应用。Guest教授是一位成就卓著的数学家，他目前是变分原理(调和映射)领域的几位权威人士之一，该领域应用于数学物理中的问题，特别是孤子和规范理论。奥卡博士是环状变种方面的权威。Ohnita博士在微分几何领域有专长，特别是李群和调和映射，古田博士的专长是Yang-Mills瞬子的模空间。日本在环簇、无限维李代数和可积系统方面处于世界领先地位。由于研究人员以前的合作证明在新的研究方向和出版物方面非常有成效，预计拟议的项目将提供类似的新的科学机会。该项目得到了NSF-CGP(全球伙伴关系中心)科学奖学金计划的支持。***