This $432,460 National Science Foundation project grant supports research at Brown University from June 2022 to May 2025 under the Mathematical and Physical Sciences program (CFDA 47.049). The research aims to advance the theory of singular integrals in non-smooth settings through consideration of weighted norm estimates, spectral theory, and dimension reduction techniques. Specifically, the project will characterize boundedness for singular operators on graphs and matrices, address the David-Semmes regularity problem in higher codimensions, and apply singular integral tools to dimensionality reduction in large data sets. The principal investigators have expertise developing theories for singular integrals in rough geometries, and this award will further those efforts with potential applications to partial differential equations, engineering, quantum computing, data science, and geometry.
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