This three-year, $239,774 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research at Stony Brook University on the uniformization and rigidity of fractal metric spaces and the complex plane. Specifically, the principal investigator will develop new techniques to better understand fractal objects with non-smooth, wrinkled or self-similar patterns applying in nature and data storage applications. This includes...
This Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides $464,902 to the University of Connecticut (UConn) to establish an Research Experiences for Undergraduates (REU) site focused on fractals and stochastics. The 3-year program will engage approximately 10 undergraduate students annually in intensive 10-week research projects that advance knowledge across areas such as fractal differential equations, stochastic...
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 $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...
The National Science Foundation (NSF) awarded a $343,850 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of Cincinnati. This 3-year grant, effective September 1, 2024, will fund research to develop new mathematical tools for analyzing the large-scale geometric behavior of non-smooth metric measure spaces, which have diverse applications across fields like fluid mechanics, neurophysiology, and fractal geometry. The project aims to enhance the...
The University of Connecticut will use $348,009 in funding from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) over a three-year period from September 2021 through August 2024. The Project Grant award will support research on "Invariant Metrics on Complex Manifolds" to promote progress in mathematical sciences and strengthen the nation's scientific enterprise. The funding will enable investigation of major problems in these fields...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides $350,358 to the University of Connecticut (UConn) to investigate geometric boundary value problems in general relativity. The research aims to advance understanding of the universe's structure by revealing connections between geometric PDEs and properties of the Laplace equation. Specifically, the project will address long-standing conjectures related to...
This Project Grant award from the National Science Foundation (NSF) Division of Mathematical Sciences supports research on the theory of dynamical systems and conformal dynamical systems. The award, totaling $262,205 over 3 years starting on August 1, 2024, will fund work to address longstanding conjectures and open new research directions in this field. The project will leverage tools from complex analysis, hyperbolic geometry, and arithmetic geometry to study moduli spaces of one-dimensional...
This Project Grant from the National Science Foundation Division of Mathematical Sciences provides $278,485 to support research on rectifiability and fine geometry of sets, Radon measures, harmonic functions, and temperatures through July 2025. Funded under the Mathematical and Physical Sciences program (CFDA 47.049), this award will advance four interconnected lines of inquiry. Researchers at the University of Connecticut will develop novel quantitative methods to study the geometry of...