Project Grant 2452649

This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) provides $300,000 to the University of California, Los Angeles (UCLA) to conduct research on dynamic free boundary problems. The project will analyze motions of physical interfaces, such as water freezing into ice, water droplets wetting surfaces, and tumor growth, in order to better understand the critical scales and singularities that arise in these processes. The research aims to develop new mathematical frameworks and methods to investigate these complex, nonlinear, and nonlocal problems. Key focus areas include studying the Stefan problem using optimal transport and particle system perspectives, modeling droplet motion on surfaces with microscopic defects, and analyzing tumor growth models with density constraints. This award supports collaborative research involving students and researchers, with the goal of advancing fundamental scientific knowledge and potentially translating findings to real-world applications in areas like materials science, fluid dynamics, and cancer biology. The project will be conducted over a 3-year period from July 2025 to June 2028.