RTG: Training Tomorrow's Workforce in Analysis and Applications

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Twelve faculty members at Duke University will lead postdoctoral fellows, graduate students, and undergraduates in a collection of Research Training Group activities designed to enhance research skills and deepen educational and training experiences. Activities including summer schools, undergraduate research conferences, seminars, professional development events, and innovative courses will draw in a broad population of students and junior researchers. The undergraduate students will be welcomed early to the exciting world of applications of mathematics and mathematical research. The project will seek to promote the mathematics major at the University and connections of mathematics to practical applications, with a focus on recruitment of students of disadvantaged backgrounds. The graduate students and postdocs will benefit from a vibrant research atmosphere, innovative teaching options, and professional development workshops. Graduate students will have access to industry internships, and postdoctoral fellows will gain experience in mentoring graduate and undergraduate students in vertically integrated research projects. This in-depth training will be facilitated by a broad set of existing successful programs and by novel initiatives designed to raise effectiveness of recruitment, education, and research.The RTG team is an interconnected research group in Analysis, Probability, Differential Equations, and Computational Mathematics, including experienced senior faculty who are leaders in their fields, active mid-career mathematicians, and early career dynamic researchers. In modern mathematics, analytic and probabilistic tools and techniques play a crucial role in a broad range of directions. The research themes for this project include challenging analysis questions (such as the Clay Institute millennium prize problem on the Navier-Stokes equation), as well as new applied analysis and probabilistic questions arising from modern applications (such as image processing, machine learning, and biological modelling). Among others, research training themes include: PDE of fluid dynamics, singularity formation, stochastic forcing; inverse problems and imaging; PDE analysis for machine learning; modeling and analysis of complex systems, with applications to life sciences; interfacial dynamics and free surface problems in materials science. The RTG graduate students and postdoctoral trainees will be exposed to the most recent advances in important research directions, and they will be trained to combine cutting edge analytic, probabilistic, and computational tools with the intuition and broad expertise of an applied mathematician.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.