Project Grant 2451909
- The National Science Foundation Division of Mathematical Sciences awarded a $193,218 Project Grant to The University of Kentucky Research Foundation from August 15, 2021 through July 31, 2024. The grant supports research titled "CLUSTER ALGEBRAS AND CATEGORIFICATION" under the Mathematical and Physical Sciences program (CFDA 47.049). This three-year Project Grant will fund mathematical research into cluster algebras and categorification at The University of Kentucky. Cluster algebras...
- 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...
- The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $300,000 Project Grant to the Regents of the University of Michigan under the Mathematical and Physical Sciences program (CFDA 47.049) to pursue two lines of investigation related to cluster algebras and cluster varieties. The first line of investigation involves constructing cluster structures on braid varieties, Richardson varieties, and related geometric spaces that have applications in representation theory and...
- The National Science Foundation (NSF) awarded a $180,935 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) to the University of Alabama. The grant, awarded on August 1, 2023, will fund research into cell decompositions of quiver grassmannians, which are related to cluster algebras. This research aims to provide a topological explanation for positivity in cluster algebras, which have connections to various areas of mathematics, physics, and other fields. The project...
- This $313,823 Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research in Brill-Noether theory to advance the study of curves in algebraic geometry. The research program includes undergraduate research opportunities through the Math Lab at the University of Kentucky, as well as establishing an annual workshop for the Kentucky-Ohio Algebra Alliance to foster a community of mathematicians working in...
- This National Science Foundation (NSF) Project Grant Award, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $210,000.00 in funding to the University of Maryland, College Park to support research on the interplay between polylogarithms, cluster algebras, and hyperbolic geometry. The key objectives are to investigate key conjectures, find new examples of hyperbolic manifolds, and compute invariants using cluster coordinates. The project will involve both graduate and...
- The National Science Foundation (NSF) awarded a $145,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of Chicago. The grant supports research into the relationship between algebraic K-theory of fields, multiple polylogarithms, and cluster structures. The project aims to uncover new connections between these mathematical concepts, with potential applications in number theory, topology, and mathematical physics. Key objectives include proving...
- This $210,000 Project Grant awarded by the National Science Foundation Division of Mathematical Sciences under the CFDA Program 47.049 "Mathematical and Physical Sciences" will fund research in algebraic combinatorics and braid varieties. The project aims to use algebraic methods to produce new combinatorial results with applications in areas like cryptography, protein folding, high-energy physics, and quantum computing. Specifically, the funds will support exploring the use of braid...
- This $199,786.00 Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research in combinatorial representation theory by Dartmouth College. The project aims to develop efficient computational algorithms that use combinatorial tools to analyze how algebraic representations can be combined, with potential applications in fields like computer vision, quantum physics, and fast matrix multiplication. Key objectives...
- This National Science Foundation (NSF) Project Grant award under the Mathematical and Physical Sciences program (CFDA 47.049) provides $210,000 in funding to The Trustees of Smith College to support research on combinatorial models in representation theory, geometry, and analysis. The key focus areas of the research project include optimizing and analyzing two types of edge-labeled graphs: webs from knot theory and representation theory, and algebraic splines from applied mathematics. The...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049) provides $266,401 to The University of Kentucky Research Foundation to study two classes of objects related to the theory of cluster algebras. The first objective is to develop a thorough understanding of SL_k friezes and tilings, which are combinatorially defined arrays of numbers connected to Grassmannian cluster algebras. The second aim is to classify algebras of finite Cohen-Macauley type and derive a new combinatorial model for their Cohen-Macauley categories using dimer models. The project will leverage connections between cluster algebras, representation theory, and combinatorics to advance knowledge in these intersecting areas of mathematics and contribute to education and international collaborations. The award has a performance period from August 1, 2025 to July 31, 2028.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $266.4k | 7/31/25 |