Project Grant 2501558
- This $330,000 federal Project Grant award from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) supports research and education activities at Yale University aimed at developing a fundamental understanding of quantum phases of matter. The key products and services to be delivered under this 3-year award include: Systematic development of a theory for new types of non-local observables, called "disorder operators", that can probe the fluctuations of...
- This $330,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research into quantum groups, W-algebras, and Brauer-Kauffmann categories, with a focus on understanding the underlying mathematical symmetries that govern natural phenomena. The principal investigator will develop emerging theories and applications of I-quantum groups, including exploring braid group actions, Drinfeld presentations, and...
- This Project Grant award of $149,002 was provided by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049). The award will fund research at the University of Iowa to extend the foundations of representation theory of finite dimensional associative algebras to the setting of algebras in tensor categories. This work aims to broaden participation in mathematics by engaging a diverse group of doctoral students in...
- This $299,996 Project Grant award from the National Science Foundation's (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental mathematical research by a team at Utah State University. The project aims to develop new algebraic and geometric tools to formalize and advance the mathematical theory underlying quantum physics, particularly in low-dimensional topology and the theory of quantum invariants. The key products and...
- This Project Grant award of $300,000.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research at Yale University to develop new mathematical tools for understanding the dynamics and rigidity of complex mathematical systems. The work aims to advance the frontier of pure mathematics, with a focus on exploring infinite-volume homogeneous spaces and the dynamics of Kleinian groups, Anosov subgroups, and arithmetic lattices. Expected...
- This $267,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research by the Massachusetts Institute of Technology (MIT) on tensor categories, quantized algebras, and the analytic Langlands correspondence. The research will focus on studying ordinary and tensor categories, some of which arise from representation theory and others that do not. This will include investigating non-integer rank generalizations of...
- This National Science Foundation (NSF) Project Grant, awarded under the Mathematical and Physical Sciences program (CFDA 47.049), provides $172,247 to support collaborative research on small quantum groups, their categorifications, and topological applications. The research aims to bridge the gap between 3D topological quantum field theories and our 4D universe, with a focus on developing homological invariants of 3D and 4D manifolds. The project will involve students and postdocs,...
- This $270,000 Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research in geometric representation theory and symplectic geometry at the University of California, Berkeley. The research aims to develop new tools and solve open problems in these mathematical fields, which draw inspiration from theoretical physics. Key research themes include investigating the cocenter of the affine Hecke category,...
- This Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program will support research in the fields of algebra and representation theory, with connections to theoretical physics. The USD 281,548 award to Utah State University will fund three related research projects that aim to advance the mathematical understanding of quantum field theory in two and three dimensions. The research will develop new connections...
- This federal Project Grant award, valued at $150,000.00, was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award supports research by Yale University to explore connections between foliations, flows, dynamics, and hyperbolic geometry in low-dimensional settings. Key objectives include advancing the understanding of the intricate relationships between geometry and dynamics, particularly in surface and 3D...
This $260,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support fundamental research into representations of quantizations and their associated categories of representations. The key products and services to be delivered under this award to Yale University include: Studying categories of highest weight modules over affine quantum algebras, establishing derived equivalences between categories corresponding to different parameters, and relating their t-structures. Relating several categorical versions of the elliptic Hall algebra and proving derived equivalences between them. Seeking a conceptual geometric understanding of unitary representations of complex semisimple Lie groups. The project also involves training young mathematicians and producing books/survey articles to benefit undergraduate and graduate students. This award reflects NSF's mission to advance scientific knowledge and understanding of major problems facing the nation through fundamental mathematical and physical sciences research.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $260.0k | 7/28/25 |