Project Grant 2142221

This Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research on the connections between fractals and Fourier transforms. The $150,000 award to the San Jose State University Research Foundation will fund a 3-year research project to investigate topics such as the construction of fractal Salem sets, calculation of fractal Fourier dimensions, and the optimality of Fourier restriction on fractals....

This three-year project grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program provides $299,292 to the University of Wisconsin-Madison to support research into complex methods in spectral and scattering problems. Specifically, the award will fund investigations into the non-linear Fourier transform and its relationship to scattering theory for Dirac systems of differential equations, which model spin-1/2 particles. Researchers will study questions of...

This $160,000 National Science Foundation project grant supports research at Emory University to develop mathematical tools for reconstructing spacetime structure in cosmology and Lorentzian geometry from May 2022 to April 2025. Specifically, the investigator will advance techniques to recover astrophysical phenomena such as gravitational waves, black holes, and cosmic strings from observational data like the cosmic microwave background. The research encompasses integral geometry, partial...

This federal Project Grant award of $210,000.00 from the National Science Foundation (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports research by Wichita State University exploring the connections between algebraic number theory, Fourier analysis, and fractal geometry. The key products and services to be delivered under this 3-year award, running from July 2025 to June 2028, include: advancing the understanding of Fourier decompositions for singular mathematical objects,...

This $196,344 National Science Foundation project grant supports research at Carnegie Mellon University exploring fundamental questions at the interface of harmonic analysis and number theory. Specifically, the grantee will pursue bounds for discrete variants of continuous operators in harmonic analysis involving integration over curved subvarieties. The grantee will also develop refined number theoretic techniques to bound several operators, including multilinear spherical variants, variants...

The Research Foundation of the City University of New York (RFCUNY), doing business as Rfcuny - City College, will receive $223,727 through June 2026 under a Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049). The grant will support research into the uniformization of non-uniform geometries, including fractal and random objects. The principal investigator will adapt and extend conformal uniformization and welding techniques to...

This Project Grant from the National Science Foundation's Mathematical and Physical Sciences program totaling $509,874 will support research and educational activities related to the frequency function method in elliptic partial differential equations and harmonic analysis at Stanford University from July 1, 2023 to June 30, 2026. The principal investigator will study local properties of solutions to elliptic partial differential equations and their gradients using the frequency function tool....

This $369,910 National Science Foundation project grant supports research into the geometry of sets and measures in Euclidean and non-Euclidean spaces at Stony Brook University from June 1, 2022 to May 31, 2025. The awardee will investigate mathematical analogs to organizing and visualizing large data sets, transferring analysis tools from low-dimensional to higher-dimensional settings. Specific activities include exploring quantitative uniform rectifiability theory in novel metric spaces,...

This three-year National Science Foundation Project Grant of $242,441 supports analytic and probabilistic methods research in geometric functional analysis at Carnegie Mellon University from June 2023 through May 2026. The award aims to advance understanding of existing methods and develop new approaches heavily involving probabilistic and analytic ideas to quantitatively study geometric properties of infinite dimensional linear spaces through their finite dimensional subspaces. Key research...

This federal Project Grant award, valued at $170,814, was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program. The award supports collaborative research by Drexel University on "Emerging Applications of Self-Similarity in Dynamical Networks." The research aims to bridge analytical theories of fractals and differential equations with applications in network science. Key objectives include developing new tools for...