Project Grant 2543311
- Federal Project Grant Award Summary The National Science Foundation's Division of Mathematical Sciences awarded a $199,999 Project Grant to the University of California, Irvine, effective September 1, 2025, through August 31, 2028, under the Mathematical and Physical Sciences (CFDA 47.049) program. The award supports fundamental research on Ricci flow and Ricci solitons, mathematical processes that model geometric evolution similar to heat diffusion across surfaces. The principal investigator...
- The National Science Foundation Division of Mathematical Sciences awarded $100,000 to The Regents of the University of California, doing business as University of California, Berkeley, on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049). The project studies singularity formation and resolution in two central geometric flows: Ricci flow, which evolves the geometry of a space, and mean curvature flow, which evolves surfaces. Research activities include...
- 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 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,...
- The National Science Foundation Division of Mathematical Sciences awarded the University of California, San Diego $106,398 on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to investigate higher multiplicity singularities in geometric variational problems. The project will establish foundational regularity theories for singularities arising in three geometric variational problems: minimal surfaces, the two-phase free boundary problem, and mean curvature...
- Grant Award Summary The National Science Foundation (NSF) Division of Mathematical Sciences awarded a Project Grant totaling $199,056 to Columbia University for research on "Nonlinear Geometric Flows: Singularity Analysis, Ancient Solutions and Regularity" under the Mathematical and Physical Sciences (CFDA 47.049) program. The award, effective September 1, 2025, through August 31, 2028, supports fundamental mathematical research investigating singularity formation in partial...
- 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...
- The National Science Foundation Division of Mathematical Sciences awarded the University of California Irvine $299,999 on August 15, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to conduct theoretical research on discrete approximation, analyzing functions of many yes/no variables and their continuous analogues in discrete and Gaussian spaces. The project investigates how much information is required to learn low-complexity functions, how well complicated functions...
- 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 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...
The National Science Foundation Division of Mathematical Sciences awarded the University of California Irvine $288,563 on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to support research into Ricci flow, Ricci solitons, and geometric evolution of curved spaces. The recipient will study fundamental questions in Ricci flow and singularity formation, with emphasis on understanding geometric models that arise near singularities—particularly those with cylindrical character at large scales—and extending techniques through singularities in higher dimensions. Research will also investigate how positive scalar curvature constrains the global topology of open three-dimensional spaces. Two primary directions structure the work: first, development of sharp asymptotic estimates near cylindrical ends in asymptotically cylindrical ancient solutions and singularity models, aimed at obtaining Taylor-type expansions to arbitrarily high order and contributing to classification of asymptotically cylindrical Ricci flows and higher-dimensional models; and second, study of open three-dimensional manifolds with positive scalar curvature using generalized singular Ricci flows. The project will support graduate coursework, undergraduate research mentoring, workshops, and outreach activities for student and early-career researcher development. Work is performed in Irvine, California, with a period of performance from September 1, 2026, through August 31, 2031.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $288.6k | 7/22/26 |