Nonnegative Matrix Theory: Generalizations and Applications

This workshop, sponsored by AIM and the NSF, will be devoted to the study of nonnegative matrices and their generalizations.

Nonnegative matrix theory is the study of matrices whose entries are nonnegative numbers. It is an important area of mathematics that has been built up from the illustrious Perron-Frobenius Theorem and has largely been driven by applications. Generalizations of nonnegative matrix theory typically fall into two related categories: Studying operators with Perron-Frobenius properties in various algebraic settings, and generalizing entrywise nonnegativity to other types of nonnegativity, e.g., with respect to a convex cone. This workshop will bring together individuals with experience and interests in classical nonnegative matrix theory, as well as in a variety of generalizations and applications. Specifically, the workshop will focus on the following areas:

1. Spectral properties of nonnegative matrices. Of particular interest is the peripheral spectrum of a nonnegative matrix and the associated eigenspaces.
2. The inverse eigenvalue problem for nonnegative matrices. Review, apply and extend recent techniques and developments toward a solution to this fundamental problem.
3. Eventually nonnegative matrices. Obtain practical characterizations and pursue a theoretical analysis applicable to the study of positive linear (control) systems.
4. Nonnegative matrices over cones. Examine the role and consequences of the above issues to the theory and applications of cone nonnegativity.
5. Matrices in the Max Algebra. Develop a comprehensive Perron-Frobenius theory of nonnegative matrices under max algebra rules and, in particular, study combinatorial aspects of the associated Perron eigenspaces.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than August 1, 2008. Applications are open to all, and we especially encourage women, underrepresented minorities, junior mathematicians, and researchers from primarily undergraduate institutions to apply.

Before submitting an application, please read the AIM policies concerning participation and financial support for participants.

For more information email workshops@aimath.org

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