Algebraic and Analytic Methods in the Mathematical Sciences

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This REU Site features simultaneous programs in algebra and applied analysis, each emphasizing computer-assisted collaborative experimentation. The analytic component is concerned with problems in the filtering, detection, and compression of signals. These questions naturally arise in many real-world settings, and the primary mathematical technique used by the students in this study is wavelet analysis. Typical student projects involve satelite transmission of meteorological data, compression and storage of fingerprint images, and fuel burnout in rocket engines. Both symbolic and numeric computations are needed for these investigations. The algebraic component is focused on matrix solutions to finite systems of noncommutative algebraic equations and on related computational issues. These algebraic systems usually define more abstract structures (e.g., groups, Lie algebras, or generalizations thereof), and have played an important role in modern mathematical physics. Typical student projects focus on the irreducible representations of quantum groups and Lie superalgebras, and on the generation of generic matrix algebras. Symbolic computation plays akey role throughout.Additional projects will be organized in conjunction with research seminar courses sponsored by the department's NSF VIGRE grant.