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

在这个由国际科学与工程办公室美洲项目资助的美国-巴西合作项目中，贝茨大学的Wong将与圣保罗大学的Daciberg L. Goncalves、Fernanda S. Cardona和Lucilia D. Borsari就拓扑不动点理论的主题进行合作。主要目的是研究基本群和尼尔森数的计算。尼尔森不动点理论已经推广到许多不同的场景，其中有(i)尼尔森巧合理论和（ii）等变尼尔森不动点理论。提议的项目试图解决一个在文献中尚未广泛研究的更普遍的巧合理论。将采用障碍理论、群上同调、群论和低维拓扑等新技术，从而将其与其他主流研究领域联系起来。这个项目的结果应该对群论、拓扑学和分析有影响，这反过来可能会应用于解决问题的技术，如偏微分方程。通过将本科生纳入该项目，PI将把一位年轻的数学家引入一个被认为对本科生来说很难的领域。这名本科生是一名女性，巴西有两名数学家是女性。该项目将促进PI与两个新合作者Borsari和Cardona之间的合作关系。

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.