Harmonic Analysis and Its Applications

Harmonic analysis and its applications is a central, broad, and burgeoning area on the international mathematical landscape. In the Department of Mathematics it is represented by the Norbert Wiener Center with its mission to develop harmonic analysis in the context of vital industrial technologies, and, in turn, to enhance these technologies by virtue of fundamental, deep, applicable harmonic analysis. The Norbert Wiener Center is the mathematical edifice to address Mathematical Engineering in the 21st century. There is no doubt that Mathematical Engineering will be to today's mathematics departments what Mathematical Physics was to those a century ago.

Whereas Mathematical Physics was an impetus for the study of differential equations and numerical analysis in mathematics departments of the 20th century, the Norbert Wiener Center will provide state of the art research in areas such as waveform design for radar and communications, and sigma-delta quantization for multifunction systems which are central to next generation government programs.

The present applicable expertise of the Norbert Wiener Center includes auditory signal processing, fMRI, fast imaging algorithms, periodicity and quantum detection methodologies, thin film analogue image processing, remote sensing, p-adic wavelet theory, uncertainty principle inequalities, and medical imaging. This expertise is based on strong mathematical research in classical and abstract harmonic analysis, wavelet and time-frequency theory, multidimensional nonuniform sampling, geometric frame theory, Grassmannian codes, and mathematical signal processing. The Norbert Wiener Center is primed to address new mathematical problems and provide mathematical direction in areas such as nanotechnology, "smart" sensor systems, and optical communications. The Center believes in the importance of continued strong theoretical underpinnings; and it deals interactively with major industrial and government research laboratories on cutting-edge concepts in Mathematical Engineering.