Conference: CBMS Conference: Strong Matrix Properties and the Inverse Eigenvalue Problem

This award supports the NSF-CBMS regional conference titled Strong Matrix Properties and the Inverse Eigenvalue Problem to be held July 28 to August 1, 2025 at Eastern Michigan University. The ten main lectures will be delivered by Bryan Shader of the University of Wyoming and Helena Smigoc of University College Dublin. In addition to participants invited from regional research colleges and universities, the organizers will reach out to a a wide range of invitees nationally.

The conference will provide early-career researchers and graduate students with access to cutting edge research tools and ideas, and established researchers will benefit from learning new ideas and incorporating strong matrix properties into their work.

By utilizing strong matrix properties modeled on the Strong Arnol'd Property, the principal lecturers have made impressive advances in the past five years in the study of the Inverse Eigenvalue Problem. These new strong properties have also energized significant progress in the study of related matrix invariants, such as maximum multiplicity of an eigenvalue and minimum number of distinct eigenvalues, and they have led to new connections with graph minors and graph propagation procedures.

These connections have also given rise to new matrix theory questions and results; new forbidden minor characterizations; new minor-monotone graph parameters; and new graph theoretic questions and results. The conference lectures will survey this rich subject and provide participants with the tools needed to explore this fruitful, new, and evolving area of mathematics. The conference website is https://sites.google.com/emich.edu/cbms.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.