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 $299,877 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research at Yale University across two major areas. In the first part, the Principal Investigator (PI) aims to prove new formulas for solutions to an equation describing the geometry and curvature of space-time, first studied by Einstein. The second part focuses on studying two-dimensional systems with scale invariance, which the PI will analyze by...
This National Science Foundation (NSF) Project Grant award under the Mathematical and Physical Sciences (CFDA 47.049) program seeks to advance the understanding of dynamical systems and the evolution from ordered to chaotic behavior. The $249,103 award to the Research Foundation of the City University of New York, effective July 1, 2024 through June 30, 2026, will support research aimed at developing new conceptual ideas, approaches, and theoretical frameworks to transcend the limitations of...
The National Science Foundation (NSF) awarded a $369,218 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of California, San Diego (UCSD) to develop analytical methods for approximating the state of certain dynamical systems. The project aims to advance the understanding of quantitative aspects of the analysis of dynamical systems, with a focus on rigidity phenomena in the dynamics of group actions on structured spaces. Key research areas include...
This $240,606 Project Grant award from the National Science Foundation's (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research at the intersection of combinatorics, probability, and other fields. The project, led by researchers at New York University, explores threshold phenomena in random discrete structures and asymptotic enumeration problems on expander graphs. Key objectives include proving the "Second...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $200,000 to conduct fundamental research on mathematical models that describe complex interactions, growth, and motion in irregular environments with stochastic unpredictability. The goal is to discover general mathematical laws that govern such systems, which have implications for a wide range of real-world phenomena including traffic, communication networks,...
This $300,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research to develop new tools for studying the geometry and dynamics of physical systems. Key research focus areas include: Investigating the existence and properties of periodic orbits in four-dimensional phase spaces with three-dimensional energy levels Studying the geometry of phase spaces to determine when dynamical systems are equivalent...
The National Science Foundation (NSF) awarded a $149,265 Project Grant under its Mathematical and Physical Sciences (CFDA 47.049) program to Yale University. The grant, awarded on June 1, 2024 with a completion date of May 31, 2027, supports research focused on the mathematical foundations of nonlinear and disordered systems, with a specific emphasis on the study of solitons and their applications in quantum physics, chemistry, and materials science. The project aims to establish new...
This $100,972 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports fundamental research on nonlinear partial differential equations and their applications in fields such as crystal growth, combustion, and game theory. The primary investigator (PI) will study the regularity, large-time behavior, and qualitative properties of solutions to these equations, which have connections to areas like the calculus of...
This Project Grant award of $254,498 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports three research projects at Princeton University focused on advancing the mathematical understanding of Gibbs measures and their dynamics. The principal investigator and collaborators are pursuing research at the interface of partial differential equations, probability theory, and differential geometry to address open problems in areas such as the...