Project Grant 2501658
- This Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program provides $250,000 in funding to Brown University to conduct research on the geometry of algebraic curves and their moduli spaces. The key research objectives include: Studying the interpolation of algebraic curves through special configurations of points, including how the curves behave as the points specialize onto hyperplanes or collide....
- This Project Grant award, valued at $250,000.00, was provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program to Brown University. The primary focus of this 3-year project is to conduct research in the areas of moduli theory and birational geometry within the field of algebraic geometry, which has important applications in coding, industrial control, computation, and theoretical physics. Key research activities include studying the...
- This Project Grant award of $225,000 from the National Science Foundation (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research by the Trustees of Boston University to study methods for determining the finite set of rational points on curves of genus 2 or higher, regardless of Jacobian rank. The research will focus on computing Selmer sets in depth 2 and 3 for new classes of curves, building on the work of Kim's nonabelian Chabauty program. The project will also...
- This three-year Project Grant from the National Science Foundation's Mathematical and Physical Sciences program, totaling $210,000, will support research into the geometry and arithmetic of Brill-Noether loci and curves. Specifically, the award recipient, Brown University, will initiate an arithmetic Brill-Noether theory program to elucidate the structure of rational points on Brill-Noether loci in the Picard variety of a curve, with applications to determining low degree points on curves...
- This $150,000 federal Project Grant award from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) to Brown University supports research on compactifications of moduli spaces and their tropicalizations within the field of algebraic geometry. The research program will develop and employ modern techniques to make new progress on the study of moduli spaces, which are parameter spaces for certain geometric objects with deep connections to mathematics, physics, and...
- This $300,000 National Science Foundation Project Grant, funded under the Mathematical and Physical Sciences program (CFDA 47.049), supports research at Wake Forest University focusing on elliptic curves with unexpected arithmetic properties revealed through their representation as distinguished points on modular curves. The Principal Investigator will develop new tools to identify such unusual elliptic curves by exploiting the geometry of modular curves and associated algebraic structures....
- This Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides $249,338 to Brigham Young University to support fundamental research on number theory problems and the study of L-functions. The key products and services to be delivered include: Studying a deep conjecture on rational points on an infinite family of curves known as Erdos-Selfridge curves, using a novel "mass increment" argument inspired by additive...
- This Project Grant award from the National Science Foundation's (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049) provides $200,000 to support research at Boston University from September 1, 2024 to August 31, 2027. The research aims to explore new theoretical frameworks for the quadratic Chabauty method, compute invariants measuring curve complexity, and introduce new tools to study the Ceresa cycle, a fundamental...
- This $260,000 Project Grant awarded by the National Science Foundation's (NSF) Division of Mathematical Sciences aims to advance the understanding of algebraic points on mathematical varieties. The primary research focus is on characterizing the arithmetic and local properties of algebraic points on curves, with complementary projects exploring higher dimensional varieties such as surfaces. The award also supports mentoring and training of early career mathematicians, particularly from...
- This $200,000 Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports the continued research of the Principal Investigator at Brown University. The research aims to advance understanding in geometry and dynamical systems, with a focus on optimal paper geometry, geometric dynamics, and connections between the Four Color Theorem and triangulations. Key planned outcomes include proving the Knotted Paper Moebius Conjecture and...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $188,325 to Brown University to conduct research on rational points on modular curves and investigate uniformity questions in number theory. The research aims to advance understanding of elliptic curves, which are central to cryptography, number theory, and algebraic geometry. Key objectives include developing quadratic Chabauty algorithms to determine rational points on certain families of modular curves without relying on explicit curve equations, as well as organizing educational initiatives to develop future talent in mathematics and contribute to mathematical databases. The project will run from August 1, 2025 to July 31, 2028.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $188.3k | 7/31/25 |