This National Science Foundation (NSF) Project Grant award under the Mathematical and Physical Sciences (CFDA 47.049) Federal Grant Program supports research at the interface of Fourier analysis and geometric measure theory. The $163,054 award to New York University, with a project period from April 2024 to August 2028, will explore connections between these two mathematical fields and their potential applications to other disciplines like dynamics and number theory. Key research components...
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 National Science Foundation (NSF) Project Grant, funded under the Mathematical and Physical Sciences program (CFDA 47.049), provides $125,000 in funding to Wichita State University from August 2023 to July 2025. The research objectives are to investigate the classification of four and higher-dimensional spaces, including compact Riemannian manifolds, Einstein manifolds, and shrinking gradient Ricci solitons, whose curvature satisfies a positivity condition. Key strategies involve...
The National Science Foundation (NSF) awarded a $310,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to The Washington University's Office of Sponsored Research Services Division. The grant supports fundamental mathematical research at the intersection of analytic function theory, harmonic analysis, and operator theory. The proposed work aims to leverage "testing theorems" to address open questions in these areas, which have applications in...
This $204,372 federal Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) supports research on the potential theoretic aspects of complex geometry. The principal investigator will employ methods from potential theory, infinite-dimensional geometry, and geometric analysis to investigate a cluster of interconnected questions and conjectures in complex geometry. The project aims to advance scientific knowledge in this...
This $119,799 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research by Wichita State University (WSU) into higher-order curvature quantities in differential geometry. The key objectives are to study the Q-curvature Yamabe problem for manifolds with corners or boundaries in four or more dimensions, and investigate geometric properties and inequalities for a class of scalar invariants related to...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports research to develop new mathematical tools and understanding of the long-term dynamics and rigidity of certain infinite-volume mathematical systems. The $300,000 award to Yale University, to be completed by June 30, 2028, focuses on advancing the frontier of pure mathematics, with the goal of enabling applications in areas like data encryption, navigation, and...
The National Science Foundation (NSF) awarded a $226,465 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to North Carolina State University (NC State). The grant supports research to advance Fourier decoupling theory and apply it across disciplines including harmonic analysis, number theory, and theoretical computer science. Key goals include interpreting existing results in decoupling theory, developing new decoupling inequalities, and exploring...
This Project Grant award of $193,010.00 from the National Science Foundation's (NSF) Division of Mathematical Sciences under the CFDA 47.049 Mathematical and Physical Sciences program supports research to develop connections between number theory and physics. The project aims to explore the representation theory of quantum groups and their applications in explaining the bridge between special functions in number theory and statistical mechanics. The research will provide training opportunities...
This $115,718 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports advanced research into the algebraic and geometric properties of solutions to systems of polynomial equations. The primary goals of the project are to study the algebraic aspects of these solutions using non-archimedean geometry, investigate the complexity of curves within varieties of general type, and develop new non-archimedean...