The National Science Foundation (NSF) awarded a $250,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to The Trustees of Princeton University Office of Research and Project Administration Division, doing business as Princeton University. This grant, awarded on June 1, 2024, will fund research centered on algebraic geometry and singularities in arithmetic settings, with the goal of developing new techniques to describe higher differential forms in positive...
This $115,718 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports advanced research into the algebraic and geometric properties of solutions to systems of polynomial equations. The primary goals of the project are to study the algebraic aspects of these solutions using non-archimedean geometry, investigate the complexity of curves within varieties of general type, and develop new non-archimedean...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $110,000 Project Grant to the University of Kansas Center for Research Inc. to study the singularities of algebraic varieties and develop methods to precisely quantify the complexity of polynomial systems through the use of invariants. This 3-year grant, which runs from September 1, 2023 to August 31, 2026, will train graduate students in technical mathematical research, implementation of results using...
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 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 $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 National Science Foundation (NSF) Project Grant Award, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $210,000.00 in funding to the University of Maryland, College Park to support research on the interplay between polylogarithms, cluster algebras, and hyperbolic geometry. The key objectives are to investigate key conjectures, find new examples of hyperbolic manifolds, and compute invariants using cluster coordinates. The project will involve both graduate and...
This $280,000 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research in birational geometry at New York University from April 2022 through March 2025. Specifically, the principal investigator will use methods from Galois cohomology of function fields, properties of algebraic cycles over non-algebraically closed fields, K-theory, and degeneration techniques to advance understanding of rationality and stable...
This Project Grant award, provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049), supports fundamental research in commutative algebra and algebraic geometry. The $207,142 award to Oberlin College will fund investigations into several classical algebraic structures, including differential operators, almost complete intersections, and Gorenstein ideals. The project aims to develop new homological techniques to understand the geometric...
This Project Grant award from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) provides $153,450 to Syracuse University to conduct research on singularities in commutative algebra and algebraic geometry. The research project, titled "Homotopical Methods and Cohomological Supports in Local Algebra," aims to leverage tools from homological algebra to gain deeper insights into the structural properties of commutative rings and study singularities in local...