Project Grant 2506566
- This $100,000 Project Grant awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) aims to develop a deeper understanding of the topology and geometry of four-dimensional spaces. The research will explore similarities and differences among these spaces when equipped with additional geometric structures, such as smooth, symplectic, and complex structures, using a mix of mathematical methods. Key goals include constructing exotic...
- This federal Project Grant award of $117,892 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on the geometry of mapping class groups and surface bundles, which are fundamental concepts in mathematics. The research project, conducted by the Regents of the University of California at Riverside, aims to develop combinatorial techniques for studying the geometry of these mathematical objects. Additionally, the educational...
- This Project Grant award, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), supports fundamental research into the topology and dynamics of four-dimensional manifolds with symplectic structures. The $156,571 award, spanning from September 1, 2024 to August 31, 2026, will enable the principal investigator to employ advanced mathematical tools, such as surgery on Lefschetz fibrations, Gromov-Witten theory, and family...
- This Project Grant award of $150,000.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program supports research at the University of Chicago to address two key aspects of topology. The first goal is to use analytical methods to study quantitative aspects of topology, such as the number of handles necessary for manifold representatives of homology classes, and how this contrasts with prior work on the number of simplices or volume. The second aim is to apply this...
- This two-year, $106,027 National Science Foundation Division of Mathematical Sciences Project Grant supports research into mapping class groups and transformation groups at the University of Maryland, College Park. The principal investigator and graduate students will develop new mathematical tools to study the structure of diffeomorphism groups and homeomorphism groups representing symmetries of manifolds. Previous work classified homomorphisms between such groups and proved conjectures...
- 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 $137,633 federal Project Grant awarded by the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) to the University of Chicago supports fundamental research on the geometry and dynamics of moduli spaces of hyperbolic surfaces. The key objectives are to: 1) further develop the connection between earthquake and horocycle flows on moduli spaces and quadratic differentials, 2) study the structure of optimal Lipschitz maps between hyperbolic surfaces and related...
- This federal Project Grant award of $106,928 was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program. The funding will support research by the University of Wisconsin-Madison that lies at the intersection of geometry, dynamical systems, and group theory. The key goals of the project are to: (1) prove the Singularity Conjecture for Cannon-Thurston maps, (2) study the dynamics of free group automorphisms to obtain rigidity results,...
- This Project Grant from the National Science Foundation's Division of Mathematical Sciences provides $442,140 to the University of Wisconsin-Madison under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) from September 2022 through September 2025. The funding supports research into the geometry, topology, and dynamics of curves, surfaces, and three-manifolds through investigating the mapping class group of surfaces. Specifically, the principal investigator and...
This Project Grant award of $150,000 from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports research at the University of Chicago to develop a theory of mapping class groups of closed 4-dimensional manifolds. The goal is to understand fundamental relationships between symmetries arising in different areas of mathematics, such as the connections between certain 4-dimensional spaces central in physics and collections of reflective symmetries of negatively curved spaces. The research will also train PhD students and postdocs. This award reflects NSF's mission to advance scientific knowledge and support research with potential for broader societal impacts. The project period is from September 15, 2025 to August 31, 2027.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $150.0k | 7/21/25 |