Project Grant 2405393
- 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 $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 (NSF) Division of Mathematical Sciences awarded a $400,000 Project Grant to New York University (NYU) for the period of August 1, 2023 to July 31, 2026. The grant, funded under the Mathematical and Physical Sciences program (CFDA 47.049), focuses on two key areas: Studying geometric evolution equations, specifically mean curvature flow and Ricci flow, with a focus on different aspects of regularity. This research aims to address longstanding open problems at the...
- This Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049) provides $300,000 to Yale University to advance research on singularities in minimal submanifolds and geometric flows. The two-part project aims to leverage the theory of self-expanders for mean curvature flow to establish sharp lower bounds for densities of minimal cones, and to address the fundamental question of uniqueness of blow-up limits at...
- 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...
- 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 $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...
- This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $200,000.00 to Northwestern University to conduct research on singularities in Kähler geometry and Lagrangian mean curvature flow. The award period runs from August 1, 2025 to July 31, 2027. The key objectives of the project are to: 1) Further the geometric understanding of singular Kähler-Einstein spaces and demonstrate that such spaces satisfy the RCD...
- This $234,951 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research into nonlinear partial differential equations and minimal submanifolds in Lagrangian geometry. The project, conducted by the University of North Carolina at Chapel Hill, will generate research opportunities for graduate students and facilitate the mentoring of graduate students and postdocs. The research will focus on two key areas:...
- The National Science Foundation (NSF) awarded a $339,999 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to New York University (NYU) for research on geometric analysis and complex geometry. The award supports the principal investigator's work on studying geometric structures of complex manifolds, including Calabi-Yau manifolds, and investigating the nature of singularities that arise in Ricci flow - a geometric evolution equation. The research aims to enhance...
EVOLUTION EQUATIONS IN GEOMETRY -EVOLUTION EQUATIONS ARE BASIC OBJECTS IN THE SCIENCES, DESCRIBING HOW NATURAL PHENOMENA CHANGE OVER TIME. FOR INSTANCE, MODELING OF A WIDE CLASS OF PHYSICAL PHENOMENA, SUCH AS CRYSTAL GROWTH AND FLAME PROPAGATION, LEADS TO TRACKING FRONTS MOVING WITH CURVATURE-DEPENDENT SPEED. OTHER NATURAL EVOLUTIONS LEADS TO OTHER EQUATIONS, MANY OF PARABOLIC TYPE, E.G. RICCI FLOW, AND MANY HAVE COMMON FEATURES. BROADER IMPACTS OF THE PROJECT ARE THROUGH MENTORING GRADUATE STUDENTS AND YOUNG RESEARCHERS, ORGANIZING SEMINARS, AND THE WRITING OF TEXTBOOKS AND EXPOSITORY ARTICLES. THE BULK OF THIS PROJECT CONCERNS EVOLUTION EQUATIONS. MEAN CURVATURE FLOW, AS WELL AS NEW METHODS FOR DEALING WITH THE DIFFEOMORPHISM GROUP FOR NON COMPACT SPACES WITH APPLICATIONS TO RICCI FLOW, WILL BE MAJOR TOPICS INVESTIGATED. OTHER NATURAL EVOLUTION EQUATIONS COMING FROM VARIOUS BRANCHES OF SCIENCES WILL BE STUDIED AS WELL AS PART OF THE PROJECT. THIS AWARD REFLECTS NSF'S STATUTORY MISSION AND HAS BEEN DEEMED WORTHY OF SUPPORT THROUGH EVALUATION USING THE FOUNDATION'S INTELLECTUAL MERIT AND BROADER IMPACTS REVIEW CRITERIA.- SUBAWARDS ARE NOT PLANNED FOR THIS AWARD.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $133.3k | 8/14/25 | ||
| Not listed | $129.4k | 5/13/24 |