Project Grant 2450299
- 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 $201,798 Project Grant was awarded by the National Science Foundation (NSF) through its Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award will support the Principal Investigator's research on applying new techniques in algebraic geometry to study the geometry of solution sets to systems of polynomial equations. The research will focus on three main directions: cohomology of moduli spaces of stable and smooth curves, and conjectures related to hypersurface...
- 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 $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...
- This federal Project Grant award of $150,000.00 from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) will support collaborative research at Temple University focused on the intersections of geometry, topology, and number theory. The principal investigator's work aims to produce new advancements in these mathematical fields, exploring the interplay between rigid geometric phenomena and topological flexibility, as well as connections to algebraic geometry...
- This $150,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on two open problems in algebraic combinatorics that intersect representation theory and algebraic geometry. The principal investigator and collaborators aim to use combinatorics to better understand these abstract mathematical objects in a more concrete way, with potential applications in mathematics, physics, and human-machine...
- This federal Project Grant award of $300,000.00 from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) will support research on quantitative symplectic geometry in higher dimensions. The principal investigator will develop new tools and paradigms to study the quantitative aspects of symplectic geometry, including initiating the study of digital symplectic geometry to link geometric methods with numerical simulations and machine learning. The award will...
- This $150,000 Project Grant award was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The funding supports collaborative research combining ideas and techniques from several exciting areas of contemporary mathematical thought, including homotopy theory, algebraic K-theory, smooth manifolds, polyhedra, and knots. The project aims to develop new connections between these fields, with plans to classify important...
- 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 $150,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research at Arizona State University (ASU) on challenging problems in discrete spherical geometry. The project explores intricate mathematical questions related to spheres, which have broad implications across fields such as data science, communications, and materials science. Key focus areas include equiangular lines, spherical two-distance...
This $287,952 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) will fund research on lattice polytopes and their connections to graphs and networks. The principal investigator will study three classes of lattice polytopes - flow polytopes, graphical Hermite normal form simplices, and faces of symmetric edge polytopes - and analyze their geometric and algebraic properties such as volume, faces, and integer point counting. This research will expand understanding of the fundamental role that lattice polytopes play in pure and applied mathematics, with applications in areas like combinatorics, optimization, and the study of coupled systems of oscillators. The project will also involve advising doctoral students and contributing mathematical expertise to research teams in mathematics education and history of mathematics. The grant period runs from August 1, 2025 to July 31, 2028.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $288.0k | 7/31/25 |