This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049) provides $300,772 to the University of Utah to develop and analyze new computational methods for solving extremal eigenvalue problems involving geometric constraints. The research activities aim to advance discovery and understanding in computational mathematics and mathematical physics, as well as support broader applications in science and engineering....
The National Science Foundation (NSF) has awarded a $100,000 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) to Michigan Technological University. The grant will fund the development of novel finite element methods for solving nonlinear eigenvalue problems, which have important applications in science and engineering. The project focuses on recasting these problems as eigenvalue problems of holomorphic Fredholm operator functions, and developing effective...
This $129,987 Project Grant award from the National Science Foundation's Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research by The Johns Hopkins University on how the geometric properties of manifolds impact the behavior of eigenfunctions, which are the fundamental modes of vibration. The principal investigator will study "global harmonic analysis" techniques to develop improved estimates for the size and concentration of eigenfunctions, specifically...
This three-year, $245,000 Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports research into geometric optimization involving partial differential equations at Claremont McKenna College. Specifically, the awardee will study optimization problems for the p-Laplacian Poisson equation, Laplace-Beltrami operator, and Steklov eigenvalue problems, with applications in optimal radiotherapy design and free boundary minimal surfaces. The...
The National Science Foundation Division of Mathematical Sciences awarded a $330,474 Project Grant to the University of Illinois under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports research investigating new mathematical properties of eigenvalues of the Laplacian operator on positively and negatively curved geometric spaces. The research aims to identify shapes that support optimal vibrations, explain relationships between spectral properties and curvature,...
The National Science Foundation (NSF) Directorate for Mathematical and Physical Sciences awarded a $250,000 Project Grant to the California State University Long Beach Research Foundation. The grant, under CFDA Program 47.049 - Mathematical and Physical Sciences, will support a research project investigating the spectral geometry of Steklov eigenvalues. Specifically, the project will study generic properties of Steklov eigenvalues and eigenfunctions, investigate domain perturbations and...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research into the dynamic interactions between operator theory, linear algebra, combinatorics, and probability theory. The 3-year, $285,236 award to Pomona College will fund investigations into new frontiers in these interconnected mathematical domains, with a focus on engaging undergraduate students in the research. Key areas of exploration...
This $246,525 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program will support fundamental research at the University of California, Irvine (UC Irvine) in the areas of spectral theory, several complex variables, and the geometry of Laplacian eigenfunctions. The key research objectives include investigations into the inverse spectral problem, the structure of Laplacian eigenfunctions, and the asymptotic behavior of Bergman...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049) provides $220,000 to Rensselaer Polytechnic Institute (RPI) from August 1, 2025 to July 31, 2028. The award will fund the development of new fast algorithms for solving Helmholtz problems and associated eigenvalue problems. These efficient computational methods will have applications in areas such as the design and optimization of engineering devices,...
This $270,000 Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research in geometric representation theory and symplectic geometry at the University of California, Berkeley. The research aims to develop new tools and solve open problems in these mathematical fields, which draw inspiration from theoretical physics. Key research themes include investigating the cocenter of the affine Hecke category,...