Federal Grant Award Summary

The National Science Foundation's Division of Mathematical Sciences awarded a $199,999 project grant to The Leland Stanford Junior University, effective July 1, 2026 through June 30, 2028, under the Mathematical and Physical Sciences program (CFDA 47.049). The award supports fundamental research and methodological development in microlocal analysis with applications to wave phenomena in geometric settings. The principal investigator will advance mathematical techniques for simultaneously tracking the position and frequency of waves, with planned applications to wave propagation analysis, quantum fields on curved spacetimes, and scattering theory. Key research objectives include characterizing long-time and far-field behavior of electromagnetic and gravitational waves on curved spacetimes, extending prior collaborative work on asymptotically hyperbolic spaces and Kerr-de Sitter spaces to cosmologically relevant settings, and proving stability properties of rotating black hole solutions to Einstein's equations.

In addition to core research deliverables, the award emphasizes workforce development and educational contributions by supporting doctoral student research projects and training the next generation of mathematicians and scientists. The project builds on established breakthroughs in microlocal analysis approaches to linear and nonlinear problems on curved spacetime geometries, extending collaborative results from Kerr-de Sitter space to Minkowski and Kerr spaces with vanishing cosmological constants. Research activities will be conducted at Stanford University's Palo Alto, California campus.