Project Grant 2506832
- This $200,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) aims to advance the study of Einstein metrics and Ricci flows in 4-dimensional topology at the Massachusetts Institute of Technology (MIT). The project will focus on understanding and constructing 4-dimensional Einstein metrics and Ricci flows, particularly examining singularities such as orbifold singularities, cusp formation, and collapsing. This research...
- This Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) provides USD 100,000 to Rutgers, The State University to study the dynamics of cylindrical singularities in geometric flows and ancient solutions. The main objective is to understand the formation and behavior of singularities that develop in certain types of geometric equations, such as the Ricci flow and mean curvature flow, which are used to evolve geometric objects like...
- The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $141,490 Project Grant to the University of California, Santa Cruz (UCSC) under the Mathematical and Physical Sciences program (CFDA 47.049). The project seeks to study the geometry and topology of spaces with Ricci curvature bounded below, including both smooth manifolds and singular spaces. Key focus areas include investigating the fundamental groups of complete and non-compact manifolds with non-negative Ricci...
- This Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) provides $149,911 to Arizona State University (ASU) to conduct research on the mathematical analysis of noncompact and singular Ricci flows. Ricci flow is a geometric heat equation that can model diverse physical phenomena, and this project seeks to better understand the behavior of solutions in highly singular regions and extend the analytic theory of the equation. The...
- The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $399,998 Project Grant to the Massachusetts Institute of Technology (MIT) under the Mathematical and Physical Sciences program (CFDA 47.049) to fund research on singularities and rigidity in geometric evolution equations. The research focuses on geometric flows, which model the evolution of geometric objects like functions, surfaces, or Riemannian metrics over time using nonlinear generalizations of the classical...
- This Project Grant from the National Science Foundation Division of Mathematical Sciences provides $206,442 to support fundamental research into geometric structures incorporating torsion, with potential applications in mathematics and physics. Funded under the Mathematical and Physical Sciences program (CFDA 47.049), the award to the University of California Irvine from August 15, 2022 through July 31, 2025 will aid in uncovering geometric and analytic aspects of generalized Ricci curvature,...
- This federal Project Grant award of $199,056.00 from the National Science Foundation's Mathematical and Physical Sciences (CFDA 47.049) program supports research on nonlinear geometric flows and singularity analysis. The principal investigator and their team at Columbia University aim to study the singular behavior of partial differential equations related to physical phenomena like turbulence, black holes, cancer cell accumulation, and neural activity. The research will focus on understanding...
- This Federal Project Grant award from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) provides $199,999 to the University of Tennessee to conduct research on the structure and behavior of ancient solutions to Ricci and mean curvature type geometric flows. The project aims to enhance the field's impact by involving graduate students and fostering collaborations across disciplines and institutions. The research will focus on developing classification results...
- This federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research in differential equations and the geometry of manifolds. The award, totaling $223,343, will fund the principal investigator's work in three main areas: classification of gravitational instantons in 4 dimensions, understanding Gromov-Hausdorff limits of Einstein metrics in the collapsing case, and the study of higher-dimensional...
- 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 $199,999 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on Ricci flow and Ricci solitons. The Principal Investigator aims to extend the surgical construction techniques developed by Perelman to continue Ricci flows through singularities, with the goal of uncovering new geometric and topological applications. The research project has two main components: 1) classifying ancient Ricci flows that are asymptotic to cylinders, which can serve as singularity models, and 2) building on the PI's work to understand 3D open manifolds with positive scalar curvature. This research will be complemented by mentoring graduate students and organizing workshops and conferences. The project duration is from September 1, 2025 to August 31, 2028 and is being performed by the University of California, Irvine.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $200.0k | 7/31/25 |