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

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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.