Project Grant 2452760

This Project Grant award of $302,028.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049) supports fundamental research on nonlinear hyperbolic and dispersive partial differential equations (PDEs). The award aims to deepen the understanding of these PDEs, which are critical for describing natural phenomena across scales, by investigating long-term dynamics, singularity formation, and the stability of special solutions. Key research objectives include progress on the strong cosmic censorship conjecture for Einstein's vacuum equation, proving the asymptotic stability of the Skyrme model equivariant B=1 skyrmion, and attacking the soliton resolution conjecture for critical semi-linear geometric dispersive equations. The project also plans to utilize the instability mechanism of degenerate dispersion to establish enhanced dissipation for the Hall-magnetohydrodynamics equations in plasma physics. The research will provide scientific insights into gravitational singularities, soliton dynamics, and small-scale formation in plasma, while also training undergraduate, graduate, and postdoctoral researchers. The award is held by the University of California, Berkeley and runs from July 15, 2025 to June 30, 2028.