Algebraic and Analytic Methods in the Mathematical Sciences

这个REU网站的特点是同时在代数和应用分析程序，每个强调计算机辅助合作实验。 分析部分涉及信号的滤波、检测和压缩问题。这些问题自然会出现在许多现实世界的设置，和学生在这项研究中使用的主要数学技术是小波分析。典型的学生项目包括气象数据的卫星传输，指纹图像的压缩和存储，以及火箭发动机的燃料燃烧。这些调查需要符号和数值计算。 代数部分集中在非交换代数方程的有限系统的矩阵解和相关的计算问题。这些代数系统通常定义更抽象的结构（例如，群，李代数，或其推广），并在现代数学物理学中发挥了重要作用。典型的学生项目侧重于量子群和李超代数的不可约表示，以及一般矩阵代数的生成。符号计算在整个过程中起着关键的作用。其他项目将与由该部门的NSF VIGRE基金赞助的研究研讨会课程一起组织。

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.