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...
This Project Grant award, valued at $220,000.00, was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award supports research by Brown University to study variational methods in singular geometry, with applications to phenomena like classical mechanics, geodesics, and harmonic maps. The project aims to develop new analytical techniques to investigate the properties of solutions to non-linear elliptic PDEs, and...
This $210,000 Project Grant award, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), supports research on nonlinear partial differential equations, geometry, and convex analysis. The research aims to develop new analytical techniques with applications in geometry, physics, and algebraic geometry. Key focus areas include studying special Lagrangian submanifolds, Kähler-Einstein metrics, and Monge-Ampère type equations. The...
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 Project Grant award of $300,000 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on singularities in minimal submanifolds and geometric flows at Yale University. The project aims to deepen the understanding of singularities in minimal hypersurfaces and mean curvature flow, which are central concepts in a range of scientific disciplines including physics, materials science, and computer vision. The research has two main...
This Project Grant from the National Science Foundation Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $144,726 to support collaborative research in the area of symplectic geometry between Cornell University and other institutions. Specifically, the funding will advance knowledge and understanding of the relationship between the geometry of Hamiltonian systems and the combinatorics of momentum maps through investigations into the...
This federal Project Grant award in the amount of $177,469.00 was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences Grant Program (CFDA #47.049). The award will support research into the geometry of moduli spaces from low-dimensional topology and applications, with a focus on three main directions: studying higher algebraic structures in instanton Floer homology, analyzing the properties of generalized Seiberg-Witten equations, and exploring the...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides $120,000 in funding to Cornell University to support fundamental research at the intersection of set theory, topology, and other mathematical fields. The key goals of the project are to: Classify the simplest non-metrizable compact topological spaces under an additional axiomatic assumption (PFA). This leverages a new approach to building non-metrizable...
This National Science Foundation (NSF) Project Grant award under the Mathematical and Physical Sciences program (CFDA 47.049) aims to advance the understanding of key problems in the field of calculus of variations. Specifically, the $149,999 award dated August 15, 2024 supports research on the Aviles-Giga conjecture, which seeks to provide a mathematical justification for a scaling law observed in physical phenomena like thin film blistering and micromagnetics. The project also explores...
This Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program provides $137,633 to the University of Chicago to conduct research on the dynamics of moduli spaces of hyperbolic surfaces. The project aims to investigate the connections between non-Euclidean hyperbolic geometry and Euclidean geometries, leveraging tools from quadratic differentials and optimal Lipschitz maps. The research will also support professional...