Project Grant 2304818

The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $222,327 Project Grant to The Trustees of Princeton University, Office of Research and Project Administration to conduct research on the metric geometry and analysis of Einstein manifolds over a 3-year period from August 1, 2023 to July 31, 2026.

The research project will focus on investigating the degenerations and quantitative behaviors of Einstein manifolds, building on prior work by the principal investigator and collaborators that has led to breakthroughs in classifying the Gromov-Hausdorff limits of Einstein metrics on the K3 manifold and asymptotic model geometries of gravitational instantons. The project will expand this line of inquiry into higher dimensions and explore geometric structures for degenerating Einstein metrics with generic holonomy. Additionally, the project will investigate the geometry and analysis of Poincaré-Einstein spaces, examining singularity behaviors, geometric finiteness, and regularity of Poincaré-Einstein metrics. The award will also support the integration of this research with training and mentorship activities, including organizing workshops and developing new research-oriented courses for undergraduate students.