Project Grant 2331920

Brown University received a $137,778 project grant award from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The grant will fund research to develop theoretical tools in high-dimensional probability via two approaches over a three year period from June 2023 through May 2026. The first approach aims to quantify the notion of intrinsic dimensionality by exploiting situations where relevant information is contained within a smaller set of variables. The second approach focuses on representing complex systems as transformations of simpler systems. The grant also supports educational efforts including undergraduate and graduate student mentoring. The research aims to improve understanding of high-dimensional probability measures through original concepts such as intrinsic dimensionality in the context of functional inequalities, as well as new measure transportation methods utilizing stochastic processes and probabilistic flows.