REU Site: Matrix Analysis, its Applications and Related Combinatorics

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Our purpose is two-fold: (1) to introduce promising mathematics students to real research in problems of current interest, through intensive, 8-week, mentored, summer programs; and (2) to make substantial research contributions to a variety of somewhat related, unsolved problems. The research that is necessary for graduate study in mathematics, and most eventual careers in the field, is quite different from traditional undergraduate course work. Experience has shown that an honest exposure to real research, within a group of like-ability students, is very efficient for future decision making by the students and as preparation and inspiration for likely graduate study.The platform for this REU program is matrix analysis and applications, broadly defined, including combinatorics. This is an excellent source of accessible, worthwhile, and open-ended problems and a most valuable area as part of the knowledge base for future work in mathematics. The PI, through his own research program and wide variety of international contacts, generates many problems, progress on which will be of interest to the community. In addition, work is likely to continue on several large problems, with many parts, on which progress has been made in prior summers. This has in the past, and likely will in the future, generate many student-authored publications, in respected, traditional journals, that will be a lasting contribution to the field.