This National Science Foundation project grant of $428,169 supports research in harmonic analysis and partial differential equations at the University of Illinois from August 2022 through July 2025. The award is funded through the Mathematical and Physical Sciences program (CFDA 47.049). The project involves foundational research in harmonic analysis and analysis of partial differential equations with a focus on long-time dynamical properties and decay estimates. Specific areas of study...
This five-year, $209,505 Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) will support research at Montana State University on elliptic and parabolic partial differential equations. The principal investigator will advance understanding of how solutions behave for more complex PDEs that model quantum behavior, systems with microscopic structure, and time-dependent phenomena. One component involves using properties of harmonic...
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 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 $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 $276,250 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental and applied research on problems in harmonic analysis and time-frequency analysis. The project, led by Purdue University, focuses on three main themes: (1) multilinear maximal/singular/oscillatory operators, (2) multidimensional maximal/singular/oscillatory operators along variable curves, and (3) pointwise convergence of Fourier...
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 $335,000 project grant awarded by the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research in harmonic analysis and approximation theory conducted by the University of Wisconsin - Madison. The key objectives are to: (1) Investigate the regularity properties and boundedness of certain averaging operators over sub-manifolds and maximal operators on nilpotent groups within harmonic analysis. (2) Study local smoothing...
This three-year Project Grant from the National Science Foundation's Division of Mathematical Sciences, under the Mathematical and Physical Sciences federal grant program (CFDA 47.049), provides $150,000 to Bridgewater State University to support collaborative research on topics in abstract, applied, and computational harmonic analysis. The research aims to advance understanding of modern tools related to Fourier analysis and their application in data science, signal processing, and quantum...
This $224,608 Project Grant award, made by the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049), supports collaborative research on stochastic functional systems. The research aims to (i) explore long-term properties of stochastic functional differential equations, (ii) formulate new approaches to study fundamental properties of McKean-Vlasov stochastic functional differential equations, and (iii) propose a framework for functional stochastic...