The National Science Foundation (NSF) Division of Mathematical Sciences has awarded a $546,334 Project Grant to The Leland Stanford Junior University, also known as Stanford University, to conduct research on "Stability in Geometric Variational Problems." This award, under the NSF's Mathematical and Physical Sciences program (CFDA 47.049), will support efforts to advance the mathematical understanding of optimal configurations that minimize energy in various scientific and engineering applications, such as determining optimal driving routes or modeling the behavior of soap films.
The key focus of this three-year project is to investigate the notion of "stability" and its implications for studying optimal configurations, including stable minimal hypersurfaces and related problems. The research will involve mentoring the next generation of researchers, creating educational materials, and collaborating on topics such as scalar curvature and the Allen-Cahn equation. This project aims to deepen the fundamental knowledge in the field of geometric variational problems, with the eventual goal of better understanding stable Bernstein problems in higher dimensions.
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