In the past decade, the analysis of massive, high-dimensional, time-varying data sets has become a critical issue for a large number of scientists and engineers. Observations across several disciplines, by researchers studying dramatically different problems, suggest the existence of geometrical and topological structures in many data sets, and much current research is devoted to modeling and exploiting these structures to aid in prediction and information extraction. Recent work by the investigators, among others, has shown that integrating statistical methodologies with ideas derived from computational topology and diffusion geometry often leads to strikingly superior results than by conventional means. The investigators now propose to bring these methods into the mathematics/statistics curriculum and departmental structure in a formal way, by establishing a vertically integrated program of undergraduate and graduate research and education. This activity has broad support from programs within the Division of Mathematical Sciences, including Applied Mathematics, Computational Mathematics, Statistics and Topology programs, as well as Division of Mathematical Sciences Workforce Program. This involves new undergraduate courses in the core theoretical areas, graduate topics courses, an extensive summer research program for undergraduates, as well as year long seminars aimed at both graduate and undergraduate students. In addition, the investigators will disseminate their ideas via summer workshops aimed at small-college faculty, and methodology workshops directed to faculty from other large research institutions.
The need to analyze massive, complex data arises in a wide variety of scientific areas of national importance, including for example satellite image analysis, medical genomics, and internet security. The investigators propose a program of training future mathematical scientists to attack these new types of problems. The program will be vertically integrated, fostering extensive collaboration between post-docs, undergraduate and graduate students, and senior faculty, and will comprise a dynamic mixture of theoretical coursework and hands-on research activity. Participants in the program will gain valuable professional experience to distinguish them in the industrial and academic job-market.
