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Inverse eigenvalue problems for graphs

An online research community sponsored by the


American Institute of Mathematics, San Jose, California

organized by

Jane Breen, Mary Flagg, Jephian Lin, and Bryan Shader

This research community, sponsored by AIM and the NSF, focuses on combinatorial and linear algebraic problems related to inverse eigenvalue problems related to graphs. The inverse eigenvalue problems for graphs (IEP-G) is to determine if a given set of real numbers is the spectrum of a matrix with a given graph. This problem and related variants have been of interest for many years and recently developed tools have accelerated progress and opened up new lines of inquiry. Zero forcing (ZF) is a propagation process on graphs. ZF has become a fundamental concept because it represents a nice bridge between combinatorics and linear algebra. ZF has also arisen independently in quantum information processing, monitoring electrical power networks, and graph search algorithms.

The primary scientific goals of this AIM research community are to

  • use all the tools--recently developed matrix theoretic ones, combinatorial approaches developed for ZF and other tools from algebra and analysis--to make significant progress on the IEP-G; and
  • investigate new lines of zero forcing (ZF) and its variants.
This AIM research community is designed to bring a diverse group of researchers into the IEP-G/ZF area and enhance collaboration and sense of community. In particular, the community will support graduate students, early career researchers, and faculty at primarily undergraduate institutes, by providing them a network of collaborators and opportunities to expand their research interests and establish successful research programs.

Collaborative research groups to pose and attack problems related to the IEP-G and ZF will be formed with the intention of proving new mathematical results leading to research publications.

Periodic moderated problem sessions will be used to keep research moving forward, nurture collaboration and train the community in how to mold ideas into interesting mathematical questions.

The community will also host regular social events such as a monthly/biweekly coffee hour, and an website provided guiding the community to pertinent professional development resources.

If you would like to participate, please apply by filling out the on-line form. Applications are open to all, and we especially encourage women, underrepresented minorities, and researchers from primarily undergraduate institutions to apply.

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