The National Science Foundation awarded The Johns Hopkins University a $320,648 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049). The grant will support research into various aspects of the theory of partial differential equations as they relate to the dichotomy between regularity and singularity formation. The Principal Investigator will pursue research in regularity theory and geometric properties for partial differential equations arising in the theory of...
This National Science Foundation (NSF) Project Grant award provides $253,734 to The Johns Hopkins University to support research on the regularity of solutions to elliptic partial differential equations and generalized minimal submanifolds. The award focuses on two main mathematical objectives: studying unique continuation for solutions to elliptic PDEs and investigating the regularity theory for generalized minimal submanifolds. This research under the NSF's Mathematical and Physical Sciences...
The National Science Foundation (NSF) awarded a $421,998 Project Grant to the University of Chicago to support research on minimal surfaces, which are important mathematical objects with applications in physics, material science, and other fields. The funding, provided under NSF's Mathematical and Physical Sciences program (CFDA 47.049), will allow the university to study the flexibility and rigidity of minimal surfaces in various geometric spaces. The project aims to deepen the understanding of...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research on geometric variational theory and applications. The $200,000 award to Cornell University will investigate the existence of closed minimal surfaces and constant mean curvature surfaces, with potential impact across scientific disciplines. Key focus areas include resolving the "Four Minimal Spheres Conjecture," developing min-max...
This Project Grant award of $300,000.00 was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) to Yale University. The project aims to deepen the understanding of singularities that arise in minimal submanifolds and geometric flows, which are important concepts in a wide range of scientific disciplines including physics, materials science, and computer vision. The project has two main components: leveraging the theory of...
The National Science Foundation awarded a $250,573 Project Grant to the University of Notre Dame under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports research into singular structures of minimal surfaces and higher dimensional minimal hypersurfaces. Specifically, the Principal Investigator will study the singular set geometry and behavior near singularities of minimal surfaces, as well as classify certain 8-dimensional minimal hypersurfaces in Euclidean space...
This National Science Foundation award provides $114,897 to the University of Texas at Dallas under the Mathematical and Physical Sciences program (CFDA 47.049) from August 1, 2022 through July 31, 2025. The principal investigator will conduct research on the existence and properties of minimal surfaces in hyperbolic 3-manifolds. Minimal surfaces are locally area-minimizing geometric objects with applications across various fields including materials science, biology, and low-dimensional...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $399,998 Project Grant to the Massachusetts Institute of Technology (MIT) under the Mathematical and Physical Sciences program (CFDA 47.049) to fund research on singularities and rigidity in geometric evolution equations. The research focuses on geometric flows, which model the evolution of geometric objects like functions, surfaces, or Riemannian metrics over time using nonlinear generalizations of the classical...
This $234,951 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research into nonlinear partial differential equations and minimal submanifolds in Lagrangian geometry. The project, conducted by the University of North Carolina at Chapel Hill, will generate research opportunities for graduate students and facilitate the mentoring of graduate students and postdocs. The research will focus on two key areas:...
This federal Project Grant award, valued at $235,375, was provided by the National Science Foundation (NSF) through its Mathematical and Physical Sciences (CFDA 47.049) program. The grant supports research by the principal investigator at Rutgers, The State University, to develop new techniques for studying minimal surfaces and exploring their applications in topology and geometry. The key objectives of this 3-year project include discovering new minimal surfaces, studying the relationship...