Project Grant 2331400
- This $300,000 Project Grant award from the National Science Foundation (NSF) under the Computer and Information Science and Engineering (CFDA 47.070) program supports collaborative research at North Carolina State University (NC State) to develop new algorithmic approaches for efficiently and rigorously computing real solutions to systems of nonlinear polynomial equations. The project aims to advance both the mathematical theory and computational methods for solving such equations, which are...
- This National Science Foundation Project Grant award of $205,000 supports collaborative research in differential geometry and algebraic geometry at the University of Notre Dame from July 2022 through June 2025. Specifically, the award funds research into the relationship between local properties of algebraic varieties and global features of tangent spaces as points vary. Investigators will also study the implicitation problem in pure mathematics and its applications in geometric modeling and...
- This $447,875 Project Grant award under the National Science Foundation's (NSF) Computer and Information Science and Engineering (CFDA 47.070) program supports research at the University of Texas at San Antonio (UTSA) to advance the theoretical foundations for efficiently processing real algebraic sets. The key objectives are to: Design algorithms for finding complex zeros of sparse polynomial equation systems in average-case polynomial time. Investigate the relationship between description...
- Federal Grant Award Summary The National Science Foundation (NSF) Division of Mathematical Sciences awarded a collaborative research project grant of $175,000 to the University of Notre Dame, effective August 1, 2025, through July 31, 2027, under the Mathematical and Physical Sciences (CFDA 47.049) program. The project delivers fundamental research in commutative algebra focused on three primary research areas: linkage theory and the classification of algebraic varieties, minimal free...
- Federal Project Grant Award Summary The University of Notre Dame DU Lac received a $145,512 project grant awarded July 1, 2025, from the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049). The two-year award (completion date June 30, 2027) supports fundamental research in commutative algebra and algebraic geometry focused on developing new theoretical understanding and computational tools for studying parameter...
- 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 Project Grant from the National Science Foundation's ($247K) Computer and Information Science and Engineering program supports collaborative research on the complexity of semidefinite and polynomial optimization through the lens of real algebraic geometry. The research will be conducted between Purdue University as the primary awardee and Carnegie Mellon University as a sub-awardee over a three year period starting in October 2021. The grant aims to advance understanding of optimization...
- Federal Project Grant Award Summary The University of Notre Dame DU Lac received a $318,144 Project Grant from the National Science Foundation's Division of Mathematical Sciences (CFDA 47.049) awarded on July 1, 2025, with completion targeted for June 30, 2028. This award funds research in delocalized homotopy theory, a specialized area within algebraic topology focused on developing new computational tools to distinguish topological types of geometric objects through algebraic invariants. The...
- Federal Grant Award Summary The National Science Foundation's Division of Mathematical Sciences (CFDA 47.049 – Mathematical and Physical Sciences program) awarded a $150,000 project grant to the University of Notre Dame effective September 1, 2025, through August 31, 2028. This award supports fundamental mathematical research focused on understanding singularities in minimal surfaces—surfaces that locally minimize area relative to their boundaries and serve as mathematical models for physical...
- The University of Notre Dame received a $249,993 Project Grant award from the National Science Foundation Division of Mathematical Sciences on August 1, 2021 to support research titled "Collaborative Research: Generalized Cluster Structures on Poisson Varieties and Applications." The three-year award will fund research exploring generalized cluster structures on Poisson varieties and their applications. The work directly supports the goals of the NSF's Mathematical and Physical...
The National Science Foundation (NSF) awarded a $300,000 Computer and Information Science and Engineering (CFDA 47.070) Project Grant to the University of Notre Dame to develop efficient and rigorous algorithms for computing real solutions to systems of polynomial equations. The 3-year project aims to create new mathematical theories and homotopy continuation algorithms that can identify at least one or all real solutions, without needing to compute complex solutions which are often orders of magnitude larger in number. The research also plans to develop sampling methods to identify smooth points in the connected components of real solution sets for polynomial systems with infinitely many solutions. This work will advance the state-of-the-art in computational real algebraic geometry, with applications in fields like robotics, chemical reaction networks, and biological processes. The project will directly support the training and mentoring of graduate and undergraduate students, while also impacting broader curricula in this research area.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $300.0k | 12/28/23 |