This National Science Foundation (NSF) Project Grant award under the Mathematical and Physical Sciences (CFDA 47.049) program provides $300,000 to the University of Maryland, College Park to conduct research on multiscale analysis of infinite-dimensional stochastic systems. The project aims to address issues in the asymptotic behavior of infinite-dimensional systems governed by stochastic partial differential equations with multiple scales and conservation laws. Key research activities include proving the validity of the small-mass limit for stochastic damped geometric wave equations, developing an infinite-dimensional version of Friedlin-Wentcell averaging theory for random perturbations of PDEs with conservation laws, and analyzing the long-term effects of small stochastic and deterministic perturbations on complex systems. The award period is from Sep 1, 2024 to Aug 31, 2027 and will involve the participation of graduate students and postdocs, as well as the development of new graduate courses and broader community engagement.
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