ABSTRACT

This research training group (RTG) aims to develop a new generation of applied mathematicians who are experts in the areas of mathematical optimization, inversion, and data science. Trainees will gain cutting-edge knowledge and experience in visualizing, analyzing, and learning from real-world data. The RTG will strengthen the graduate and postdoctoral programs to attract top students in the nation and place them in top jobs. The investigators will diversify the recruitment with efforts at the high school and early undergraduate levels, geared towards underrepresented groups to broaden participation in mathematics. The RTG will introduce novel transformative experiences for students and emphasize on critical career transition points to attract and retain students into math-related careers. The RTG project will encourage interaction, collaboration, and mentorship between participants at different stages of their academic careers. Core examples include working with junior high and high school teachers to make math more accessible and exciting to students, vertically integrated Focused Reading/Research Groups, a Science Research Initiative to significantly increase the number of first-year undergraduates involved in research, and Polar Research Experiences on Arctic Sea ice that provide a unique hands-on opportunity for students to gather, analyze, and model their own data, closing the loop between theory and practice.

Mathematical optimization, inversion, and data science play a crucial role in applications across the sciences, engineering, and medicine. This RTG leverages the expertise of mathematics faculty in these and related areas to train and mentor students across levels ranging from high school to doctoral and postdoctoral scholars. Some of the core projects will include optimal design of metamaterials, porous media, photonics, climate modeling, machine learning, remote sensing, polar ecology, medical imaging, geophysical exploration, drug delivery and discovery, and uncertainty quantification. The RTG will introduce a new optimization-centered graduate curriculum, offer trainees at all levels significant experience working on important interdisciplinary problems in vertically integrated settings, and, mimicking successful engineering classes, a mathematical design competition to motivate students, and a thematic RTG conference to provide collaborative mechanisms between RTG participants and internationally renowned researchers. This RTG project will benefit the broader math community and beyond as the involved students and postdocs assume leading roles as researchers and educators in the 21st-century workforce.

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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