This National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) Project Grant award of $327,441 to the University of Illinois will fund research focused on challenges at the intersection of harmonic analysis, number theory, and dispersive equations. The principal investigator (PI) plans to explore connections between diverse mathematical fields, including additive combinatorics, classical Fourier analysis, dispersive equations on tori, and ergodic theory. The funded...
This Project Grant from the National Science Foundation Division of Mathematical Sciences provides $292,823 in funding from August 1, 2022 to July 31, 2025 under the Mathematical and Physical Sciences program (CFDA 47.049). The award supports research and training at the University of Chicago on nonlinear partial differential equations with stochastic dependence, homogenization in random media, well-posedness in singular domains, mean-field games, and convergence of growth models. Key areas of...
This Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental mathematical research at the University of Chicago focused on probabilistic aspects of dispersive and wave equations. The $176,355 award, made on May 15, 2025, will fund five interconnected research projects over a 14-month period ending on July 31, 2026. The key products and services to be delivered include: Extending the short kinetic time derivation...
This $100,972 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports fundamental research on nonlinear partial differential equations and their applications in fields such as crystal growth, combustion, and game theory. The primary investigator (PI) will study the regularity, large-time behavior, and qualitative properties of solutions to these equations, which have connections to areas like the calculus of...
This Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) provides $232,812 to The Johns Hopkins University from July 1, 2022 to June 30, 2025 to improve understanding of dispersive partial differential equations. Key products include research on the long-time behavior of solutions to critical scaling equations like the Schrödinger maps problem and focusing/mass-critical nonlinear Schrödinger equation. Additional work will analyze energy...
This Project Grant award for $249,454, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program, supports research conducted by the University of Alabama in two areas within mathematical analysis: harmonic analysis and partial differential equations. The key objectives are to expand knowledge in harmonic analysis and its applications to the study of partial differential equations, as well as to provide education and mentoring...
This $300,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research aimed at advancing the mathematical analysis of nonlinear partial differential equations. The research has three main focus areas: (1) studying fluid dynamics problems with free boundaries, such as water waves, tsunamis, and hurricanes; (2) investigating the dynamics of gases and plasmas under physical kinetic boundary conditions,...
This $300,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research in three canonical classes of nonlinear partial differential equations. The key objectives are to: Advance the understanding of existence, regularity, and large-time behavior of solutions for multi-dimensional Euler alignment equations, nonlinear conservation laws, and the pressure-less system. This involves developing novel...
This National Science Foundation Project Grant award of $120,720 supports research and educational activities in the field of harmonic analysis at the University of Massachusetts Lowell from September 2022 through August 2025. The award is funded through the NSF's Mathematical and Physical Sciences program (CFDA 47.049), which aims to advance scientific knowledge and understanding in these fields. Specifically, the award will support research on several topics in real and discrete harmonic...
This Project Grant award, totaling $150,000.00, was provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) to support research on asymptotic phenomena in partial differential equations (PDEs) arising in various scientific applications. The principal investigator will investigate the long-time behavior of solutions to reaction-diffusion equations in heterogeneous and random environments, study the long-time and white-noise limits of physically...