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 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...
The National Science Foundation awarded a $400,134 Project Grant to the Georgia Tech Research Corporation from the Mathematical and Physical Sciences program (CFDA 47.049) to conduct research in discrete harmonic analysis. Specifically, the awardee will analyze averages over prime numbers in abstract number field settings to gain new insights into traditionally evasive questions about prime numbers and the Goldbach conjecture. A range of questions concerning averages over prime numbers and...
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 $446,924 National Science Foundation (NSF) Project Grant, funded under the Mathematical and Physical Sciences program (CFDA 47.049), supports research into problems in harmonic analysis relating to curvature at the University of Wisconsin-Madison. Specifically, the university will investigate bounding and studying reverse inequalities for certain mathematical operators called Fourier restriction and averaging operators, where the curvature of an underlying manifold plays an important...
The National Science Foundation awarded $376,018 under the Mathematical and Physical Sciences program (CFDA 47.049) to Carnegie Mellon University for the project "Stability and Regularity: From Analysis to Geometry" from September 1, 2022 to August 31, 2025. The project focuses on using functional and geometric inequalities to explore the geometry of manifolds and domains. Such inequalities describe ground states for physical systems in acoustics and materials science. Researchers will...
This three-year, $249,990 project grant from the National Science Foundation's Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), will support collaborative research on fundamental problems in time-frequency analysis at Tufts University. Specifically, the investigators will work to solve the long-standing Heil-Ramanathan-Topiwala conjecture and related open problems arising at the intersection of abstract, applied, computational harmonic...
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 $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 Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports fundamental research in harmonic analysis and its applications. The PI at Brown University will conduct theoretical and applied research in two main areas: (1) harmonic analysis in non-doubling measure settings, and (2) applying harmonic analysis to problems in complex analysis and operator theory. This includes investigating sparse domination of...
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 defined over primes, and higher codimensional analogues. This work addresses connections to discrete geometry, lattice point counts of surfaces, and Falconer's distance conjecture. Additionally, the grantee plans to pursue sparse bounds for both continuous and discrete operators, allowing weighted estimates. The one-year project beginning July 1, 2022 advances the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) by strengthening the nation's scientific enterprise through increasing mathematical knowledge and understanding of major problems.