This three-year $350,000 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program will support research at the University of Maryland, College Park on moduli spaces of Higgs bundles, gauge theory, and related topics in complex geometry. The principal investigator will further studies on moduli spaces of Higgs bundles on Riemann surfaces, including work on parabolic lambda-connections, construction of a universal moduli space, and the asymptotic and...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $170,443 Project Grant to the University of Massachusetts Boston (UMass Boston) under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports research in "Critical Symplectic Geometry, Lagrangian Cobordisms, and Stable Homotopy Theory." The project aims to incorporate ideas from homotopy theory and category theory into symplectic geometry to prove structural results about...
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...
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...
This $177,469 Project Grant awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program supports research into the geometry of moduli spaces from low-dimensional topology and applications. The primary objectives are to study higher algebraic structures in instanton Floer homology, analyze the properties of generalized Seiberg-Witten equations, and explore applications of Kontsevich configuration space integrals in 4-dimensional topology....
This National Science Foundation (NSF) Division of Mathematical Sciences Project Grant award to Michigan State University totaling $160,279 supports research in the field of algebraic geometry. The project will explore the constraints placed on smooth nonlinear shapes from modular forms, and then examine which features persist when the shapes acquire singularities. This will require the use of more general tools called quasi-modular and mock modular forms. The project offers opportunities for...
The National Science Foundation (NSF) awarded a $333,182 Project Grant through its Mathematical and Physical Sciences (CFDA 47.049) program to the University of Wisconsin - Madison. This grant supports research at the interface of several complex variables, differential geometry, and dynamical systems. The project aims to study the smoothness of transformations on complex-valued function domains, analyze resonance phenomena and singularities, and investigate the stability of holomorphic...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $399,773 Project Grant to the University of Illinois, Urbana-Champaign to support research on the "Interactions Between Geometry, Topology, Number Theory, and Dynamics" from August 1, 2023 to July 31, 2026. The research aims to advance the understanding of topology and geometry and their connections to other areas of mathematics and computer science, including applications in data mining 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...
This $250,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research in moduli theory and birational geometry at Brown University from August 1, 2024 to July 31, 2027.
The research aims to advance the understanding of algebraic varieties and their moduli spaces, which have significant applications in fields like coding, industrial control, computation, and theoretical physics. Key focus areas...