Department of MathematicsThe Duke Mathematics Department hosts a Research Training Group (RTG) centered within the areas of analysis, probability, partial differential equations (PDE), and computation. This research and training activity is funded by the National Science Foundation grant "Training Tomorrow's Workforce in Analysis and Applications" (award DMS-2038056) beginning in July 2021. Led by 12 mathematics faculty working in analysis, probability, PDE, and computation, the RTG will engage undergraduates, graduate students, and postdoctoral fellows in a collection of activities designed to enhance research skills and deepen educational and training experiences.
The vertically-integrated RTG activities will run throughout the year and are organized around various research themes, including 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 these 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.