RTG: Mathematics of Information and Data with Applications to Science

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The big-data revolution has transformed many areas of engineering, industry, mathematics, and science. For instance, data generated through genome-wide association studies, observations from telescopes, and computational simulations on petaflop computers provide tremendous opportunities to better understand the world around us. These massive datasets also pose many challenges, and there has been an explosion of research in recent years about how to manipulate, store, and extract meaningful information from ever-larger amounts of data. Mathematical analysis, algorithms, and insights have been and will continue to be a crucial component of this research effort. This RTG project will focus on the mathematical foundations and applications of data science and will catalyze research collaborations that combine different mathematical perspectives to address emerging challenges and opportunities. The mathematical challenges of data science also present a unique and transformative opportunity to develop more systematic and integrated training for the next generation; the project will broaden and enhance the scope and quality of the educational and research training provided to graduate students and postdoctoral fellows and will involve more undergraduate students, particularly students from historically underrepresented groups, in courses and research experiences in applied mathematics, increasing the workforce trained in data science.The project focuses on research and training in the mathematical foundations of data science and its applications. The research projects have strong interdisciplinary flavor, combining fundamental stochastic, statistical, combinatorial, dynamical, and computational aspects with concrete applications. Projects will involve collaborations with domain scientists from other disciplines, including astrophysics, biology, engineering, and neuroscience. Topics will include applying machine learning and Bayesian statistics tools to deriving, analyzing, and simulating partial differential equations; designing optimal closed-loop experiments using statistical inference; advancing techniques in discrete optimization; developing combinatorial models in neuroscience; understanding random projections of high-dimensional measures; and constructing dimension reduction techniques that preserve relevant structure of large data sets. The educational activities focus on vertically integrated training of undergraduates, graduate students, and postdoctoral fellows. Training activities include a first-year seminar focused on the interface of data and social justice, enhanced undergraduate and graduate curricula, summer research experiences for undergraduates, graduate students, and postdoctoral fellows, and working groups for advanced graduate students and postdoctoral fellows. The broader impacts include the recruitment, retention, and training of a diverse cohort of applied mathematicians trained in data science. In addition, the research planned in genome-wide association studies, design of closed-loop neuroscience experiments, single-cell data alignment, image restoration, simulation of Hubble data, self-assembly, inference of dynamical brain data, and data compression and reduction aims to have impact in applications.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.