Project Grant 2203572

This three-year project grant from the National Science Foundation's Mathematical and Physical Sciences program, totaling $349,952, will support research into the curvature of four-dimensional manifolds at Stony Brook University from September 2022 through August 2025. Specifically, the principal investigator will investigate generalizations of Einstein's field equations of general relativity in the Riemannian setting without distinguishing between space and time. The research aims to determine which four-dimensional spaces admit solutions to these generalized equations. Additionally, the project will train graduate students in mathematical research through their participation and help elucidate fundamental links between curvature and topology in dimension four, including the construction of canonical metrics and understanding relevant moduli spaces and bubbling phenomena. Progress could impact fields like classical and quantum gravity as well as theoretical physics more broadly. The Research Foundation for the State University of New York will administer the award on behalf of Stony Brook University.