Project Grant 2200732
- This $313,273 Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) program will support research at the University of Nebraska aimed at settling various open conjectures in the field of commutative homological algebra. The key research areas include non-commutative analogues for DG categories, duality in Hochschild homology, homological properties of modules of finite projective dimension, Ulrich modules and sheaves, and matrix...
- This $119,093 Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports research at North Carolina State University in commutative algebra, algebraic geometry, combinatorics, and singularity theory. The research aims to develop new formulas and computational methods with applications in areas like geometric modeling, investigate the multigraded structures of algebraic varieties, and advance the understanding of...
- This Project Grant award, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049), supports fundamental research in commutative algebra and algebraic geometry. The $195,000 award will fund a 2-year collaborative research project to advance the classification and understanding of geometric objects known as varieties, which have applications in science and engineering. The key research objectives include: 1) identifying new...
- This $150,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on two open problems in algebraic combinatorics that intersect representation theory and algebraic geometry. The principal investigator and collaborators aim to use combinatorics to better understand these abstract mathematical objects in a more concrete way, with potential applications in mathematics, physics, and human-machine...
- This Project Grant award from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) supports fundamental research in commutative algebra and the study of Koszul algebras. The $277,690 award to Iowa State University, effective September 1, 2024 through August 31, 2027, will fund research on free resolutions and Koszul algebras, with applications in areas such as geometry, combinatorics, and hyperplane arrangements. Key activities include classifying new Koszul algebra...
- This Project Grant award of $317,407 from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program will support research at the University of Nebraska on the topology of 3- and 4-dimensional manifolds. The project aims to uncover deep connections between manifold theory in these dimensions, with potential applications in fields such as biology, chemistry, physics, and quantum computing. Specific objectives include proving additional cases of the Smooth...
- This Project Grant award from the National Science Foundation Division of Mathematical Sciences, under the CFDA program Mathematical and Physical Sciences (47.049), provides $165,000.00 over 3 years from August 1, 2023 to July 31, 2026 to Texas A&M University for research in commutative algebra, algebraic geometry, and algebraic combinatorics. The primary focus of the research is using combinatorial models to understand affine varieties and the algebro-geometric significance of these models....
- This Project Grant award, provided by the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049), supports collaborative research on bridging singularities in algebra and geometry across mathematical characteristics. The $109,999 award, effective August 1, 2025 through July 31, 2027, aims to deepen the theoretical foundations of commutative algebra and address problems in related disciplines such as algebraic geometry. The research focuses on singularities, or...
- This $217,000 Project Grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences supports research on computational structures in equivariant chromatic homotopy theory, with a focus on developing new techniques to advance computations related to Lubin-Tate theories and the study of homotopy groups of spheres. The award funds a range of projects that leverage recent discoveries in equivariant homotopy theory to drive progress in chromatic homotopy theory and...
- This $200,000 National Science Foundation Division of Mathematical Sciences Project Grant will support research and training in noncommutative algebra and geometry at the University of California Irvine from July 1, 2022 to June 30, 2025. The award will advance fundamental understanding of noncommutative algebraic structures that arise in geometry and physics. Researchers will develop new techniques to deduce good algebraic properties for geometrically constructed noncommutative algebras and...
This National Science Foundation Project Grant award of $282,638 provides funding from June 1, 2022 to May 31, 2025 to support research in commutative and homological algebra at the University of Nebraska. Specifically, the award will further investigations into open conjectures regarding the possible values of Euler characteristics of certain complex structures and lengths of modules of finite projective dimension. The research project involves four main topics: establishing bounds on module lengths and multiplicities of tiny complexes; constructing Ulrich modules and limiting Ulrich sequences; analyzing cones of Betti and cohomology tables where Ulrich sheaves play an essential role; and proving the non-commutative analogue of the Hodge conjecture for matrix factorizations of isolated hypersurface singularities. In addition to advancing these areas of pure mathematics, the grant provides support for related work by graduate students. The funding advances the statutory mission of the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049).
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $282.6k | 3/25/22 |