REU Site: Matrix Analysis, Combinatorics, and Applications

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The William and Mary Research Experiences for Undergraduates (REU) program seeks to initiate promising undergraduate students, from a variety of backgrounds, into productive mathematical research. This will also help to give them a useful preview of part of graduate study. In an 8-week program, carefully chosen students will be exposed to high-level, worthwhile problems in matrix analysis, combinatorics, and their applications and then mentored by experts in the process of making contributions to the understanding of these problems. The goal is two-fold: 1) to enable the students to perform sufficiently valuable research to warrant publication in respected outlets, and 2) to contribute materially to the body of knowledge about important areas of the mentioned subjects. Historically, the W&M REU program has involved quite a number of topics in this project. One of the unifying themes has been the interplay between combinatorial ideas and matrix analysis, often the role of combinatorial mathematics in the understanding of matrix analytical questions. This theme will continue. Some particular topic areas have been: 1) matrix completion problems, involving a variety of classes of matrices; 2) constraints on the multiplicities of the eigenvalues of a matrix, resulting from its graph; 3) the field of values of a matrix; 4) properties of matrices that may be inferred from the pattern of signs, or the zero/nonzero pattern of their entries; 5) totally positive matrices; and many other more specific questions. Each year, new problems are gathered from the active research programs of the principal investigators/mentors and their many collaborators.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.