Federal Project Grant Award Summary

The University of Maryland, College Park received a $200,000 project grant from the National Science Foundation's Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049), effective July 1, 2026 through June 30, 2029. This award funds fundamental research on soliton dynamics for nonlinear evolution equations, focusing on the long-time behavior of solutions to dispersive and heat-type equations that exhibit topological solitons. The research investigates how waves interact with themselves and their environment, seeking to determine conditions under which waves disperse, persist, or collapse. The intellectual products delivered through this award include theoretical analysis and mathematical insights into multi-soliton dynamics, the reduction of strongly interacting soliton systems to underlying N-body problems, and advancement toward resolving the soliton resolution conjecture—which predicts that generic solutions decompose into finite superpositions of solitons and dispersive terms.

The project provides broader impacts through research training and education of graduate students and postdoctoral researchers at the University of Maryland, College Park facility in Maryland. The mathematical and theoretical findings have potential applications across multiple technological domains, including microchip design, fiber-optic data transmission, quantum physics, and fundamental understanding of elementary particles and astrophysical phenomena such as black holes. This award exemplifies the Mathematical and Physical Sciences program's emphasis on advancing fundamental scientific knowledge while developing the nation's scientific workforce through integrated research and educational activities.