Project Grant 2154402

This three-year, $298,267 National Science Foundation Project Grant supports research at Michigan State University on non-homogeneous harmonic analysis, spectral theory, and weighted norm estimates as they relate to singular integrals. Singular integrals are mathematical objects that feature in the study of partial differential equations with diverse applications. This award will further the understanding of singular integrals in non-smooth settings through consideration of weighted boundedness for para-product operators on graphs and the David-Semmes regularity problem in higher codimensions. Results have implications for dimensionality reduction in large data sets. The work directly addresses the goals of the NSF Mathematical and Physical Sciences program (CFDA 47.049) to strengthen the nation's scientific enterprise through increasing fundamental knowledge in these fields.