The National Science Foundation (NSF) awarded a $112,949 Project Grant to The Trustees of the Stevens Institute of Technology to conduct research under the Mathematical and Physical Sciences (CFDA 47.049) program. The project, titled "Uniformization of Surfaces and Mapping Problems in Metric Spaces", aims to develop new mathematical approaches for understanding the geometry of non-smooth spaces, building on the classical Uniformization Theorem. The research will investigate methods for...
This $177,900 Project Grant, awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), supports research on discrete conformal geometry of polyhedral surfaces. The primary objective is to solve the discrete uniformization problem for all polyhedral surfaces without topological constraints. The research aims to integrate techniques from discrete and computational geometry, Riemann surface theory, convex geometry, and 3D hyperbolic...
The National Science Foundation (NSF) awarded a $285,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of Utah to conduct research on hyperbolic geometry in two- and three-dimensional spaces. The project, running from August 1, 2024 to July 31, 2027, will focus on studying the geometry of hyperbolic 3-manifolds, including investigating the renormalized volume of such manifolds and the connection to the Weil-Petersson gradient flow. The...
This $142,565 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research on the study of manifolds, or geometric objects, with positive or non-negative curvature. The principal investigator (PI) at James Madison University aims to construct new examples of such manifolds and develop new methods for proving rigidity theorems about their properties. The project also includes broader impact activities like outreach,...
This Project Grant award, valued at $137,324.00, was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award is focused on advancing the mathematical understanding of polytopes, which are geometric structures with universal importance in many areas of mathematics, including computer science, architecture, art, and philosophy. The principal investigator plans to attack various problems related to polytopes and...
This $266,696 federal Project Grant award was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program. The award supports research projects that combine mathematical analysis, differential geometry, calculus of variations, materials science, and engineering design. Key focus areas include: (i) developing mechanical theories of thin multi-dimensional films with non-zero stored energy, (ii) investigating regularity of solutions to...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a 3-year, $250,000 Project Grant to the University of Wisconsin - Madison under the Mathematical and Physical Sciences program (CFDA 47.049) to investigate moduli spaces of surfaces with additional geometric structure. The grant will fund research to solve long-standing conjectures about the geometry and topology of these moduli spaces, which are mathematical spaces that parameterize the shapes an object can take....
This $300,000 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) aims to develop innovative Artificial Intelligence (AI) tools to study polyhedra, which are fundamental geometric shapes with wide-ranging applications. The key objectives of the project include: Leveraging AI techniques like diffusion methods and reinforcement learning to generate diverse, high-quality polyhedral samples Integrating large language...
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...
This Project Grant award for $330,586, provided by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA No. 47.049), supports research on the geometric and metric properties of two-dimensional surfaces. The principal investigator (PI) at Cornell University will investigate the classification of surfaces under singular flat and hyperbolic metrics, as well as the associated moduli spaces and related mathematical...