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 funding of $226,665 to the University of Virginia (UVA) for research focused on the geometric classification and topological properties of 4-dimensional manifolds. The objectives include examining the validity of 4-dimensional topological surgery theory, studying symmetries of 4-dimensional spaces, and developing new tools for distinguishing them. The project...
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 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 National Science Foundation (NSF) Project Grant award under the Mathematical and Physical Sciences program (CFDA 47.049) provides $199,482 to the University of Illinois for research on the topology of 3-manifolds and 4-manifolds using bordered Floer homology. The award period runs from August 15, 2024 to July 31, 2027. The key objectives of the research project are to: 1) extend invariants developed in the PI's previous work to 3-manifolds with multiple torus boundary components, and use...
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 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research in differential equations and the geometry of manifolds. The award, totaling $223,343, will fund the principal investigator's work in three main areas: classification of gravitational instantons in 4 dimensions, understanding Gromov-Hausdorff limits of Einstein metrics in the collapsing case, and the study of higher-dimensional...
This National Science Foundation Project Grant of $250,000 supports research into low-dimensional topology through July 2025. Funded under the Mathematical and Physical Sciences program (CFDA 47.049), the award to Duke University will advance understanding of fundamental questions in knot theory and 4-manifold topology. Specifically, the principal investigator will investigate knot concordance problems tied to the unique properties of 4-dimensional manifolds compared to higher dimensions....
This Project Grant award of $317,407 from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program will support research at the University of Nebraska on the topology of 3- and 4-dimensional manifolds. The project aims to uncover deep connections between manifold theory in these dimensions, with potential applications in fields such as biology, chemistry, physics, and quantum computing. Specific objectives include proving additional cases of the Smooth...
This National Science Foundation Project Grant award of $104,011 provides funding from July 1, 2022 through June 30, 2024 to support research in differential topology at Rutgers University-Newark. The award is made under the Mathematical and Physical Sciences program (CFDA 47.049), which aims to promote progress in mathematics and the physical sciences. Specifically, the funding will support research into complex plane curves and their applications in 4-dimensional topology. The principal...