ABSTRACT

This Research Training Group (RTG) project is a joint effort of the Department of Applied Physics and Applied Mathematics, the Department of Mathematics, and the School of Engineering and Applied Sciences at Columbia University. It aims to create a cutting-edge research and training program in modern applied mathematics. By substantially enriching research and educational experiences for trainees, and by directly coupling into key educational and research initiatives in the School of Engineering and Applied Sciences and across the University, the activities will have a significant impact on applied mathematics education and training at Columbia. The RTG project will engage high school as well as undergraduate students from the New York metropolitan area and across the country (through the Summer Research Program), inspiring mathematical careers for underrepresented groups in the United States.

The project includes three main ingredients: (i) a group of research topics in applied mathematics at the frontier of engineering applications; (ii) a coherent mentoring-learning program on applied mathematics research and career development for undergraduate and graduate students as well as postdoctoral scholars; and (iii) a systematic plan to modernize undergraduate and graduate curriculum in applied mathematics and scientific computation. The senior investigators and the trainees will form groups to tackle challenging and rewarding mathematical and computational problems, including linear and nonlinear wave propagation in novel complex (and possibly random) structures, physics- and data-enabled algorithms for material discovery, hybrid inverse problems and imaging, mathematical theory of machine learning, harmonic analysis of large data sets, and uncertainty quantification. They will collaborate with leading engineers at Columbia to connect their mathematical and computational discoveries with applications in nonlinear optics and photonics, materials science, medical imaging, climate modeling, and general data science. The senior members of this RTG project are strongly committed to training and mentoring undergraduates, graduate students, and postdoctoral scholars. Their extensive and varied experiences in teaching and mentorship will be invaluable to the professional growth of the trainees.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

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