U.S.-Brazil Cooperative Research: Nielsen Fixed Point Theory and Related Topics

美国-巴西合作研究：尼尔森不动点理论及相关主题

• 批准号: 0334814
• 负责人: Peter Wong
• 金额: --
• 依托单位: Bates College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-04-15 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0334814&HistoricalAwards=false
• 关键词: U.S.; Brazil; Cooperative; Research; Nielsen

In this U.S.-Brazil collaborative project funded by the Americas Program of the Office of International Science and Engineering, Wong of Bates will collaborate with Daciberg L. Goncalves, Fernanda S. Cardona, and Lucilia D. Borsari of the University of Sao Paulo on topics in topological fixed-point theory. The main objective is to study the fundamental group and the computation of the Nielsen number. Nielsen fixed-point theory has been generalized to many different settings among which are (i) Nielsen coincidence theory and (ii) equivariant Nielsen fixed point theory. The proposed project attempts to tackle a more general coincidence theory that has not been extensively studied in the literature. New techniques from obstruction theory, group cohomology, group theory, and low dimensional topology will be employed, thereby relating it to other mainstream research areas.Results from this project should have impact in group theory, topology and analysis, which in turn may be applied to problem-solving techniques, such as partial differential equations. By incorporating an undergraduate into the project, the PI will introduce a young mathematician to a field that is considered difficult for undergraduates. The undergraduate student is a woman, and two of the mathematicians in Brazil are women. This project will foster partnerships between the PI and two new collaborators, Borsari and Cardona.

在由国际科学与工程办公室资助的美国巴西合作项目中，贝茨的Wong将与Daciberg L. Goncalves，Fernanda S. Cardona和Sao Paulo大学的Lucilia D. Borsari合作在拓扑定点理论中主题。 主要目的是研究基本组和尼尔森数量的计算。 尼尔森的定点理论已被推广到许多不同的设置，其中（i）尼尔森的巧合理论和（ii）nielsen nielsen固定点理论。 拟议的项目试图解决一种更普遍的巧合理论，该理论尚未在文献中进行广泛研究。 将采用障碍理论，群体共同体学，群体理论和低维拓扑的新技术，从而将其与其他主流研究领域相关联。该项目的回报应在群体理论，拓扑和分析中产生影响，而小组理论和分析也可以应用于问题解决问题的技术，例如部分差分方程。 通过将大学纳入该项目，PI将向一位年轻的数学家介绍一个被认为很难的本科生的领域。 本科生是一名女性，巴西的两名数学家是女性。 该项目将促进PI与两个新合作者Borsari和Cardona之间的合作伙伴关系。