This $390,000 National Science Foundation project grant supports research into branching processes, random partial differential equations, and their applications from September 2022 through August 2025. Funded through the Mathematical and Physical Sciences program (CFDA 47.049), this award to Stanford University will advance tools and understanding of the connections between branching processes and nonlinear parabolic equations.
Specifically, researchers will study branching Brownian motion in higher dimensions, long-time behavior of nonlinear equations arising in fluid dynamics and reaction-diffusion modeling at very long time scales, and long-time behavior of solutions to mean-field systems relevant to macroeconomics. By developing simplified models that capture dynamics of more complex systems, this work aims to validate approximations for applications in physical sciences and macroeconomics. Graduate student training will also be integrated into the research.
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