Project Grant 2606106

The National Science Foundation Directorate for Mathematical and Physical Sciences awarded the University of Maryland, College Park $300,000 on August 15, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop and analyze partial differential equation models of collective behavior in biological systems, with emphasis on nonlocal interactions and free-boundary problems.

The investigator will construct mathematical models explaining how individual-level mechanisms—chemical signaling, attraction and repulsion, growth, and crowding—produce large-scale collective patterns including clustering, swarming, tissue expansion, wound healing, tumor growth, and microbial colony spread. The work addresses limitations in classical reaction-diffusion equations by introducing a new class of models for range expansion of immotile cell colonies. Using multiscale analysis and long-time asymptotics, the investigator will derive free-boundary problems describing dynamics of Patlak-Keller-Segel type chemotaxis models with nonlinear diffusion and nonlocal interactions. The project supports education and training of students and postdoctoral researchers at the interface of partial differential equations, analysis, and mathematical biology.

Performance occurs at College Park, Maryland, with a period of performance from August 15, 2026, through July 31, 2029. The award is classified as a Project Grant assistance type.