The National Science Foundation (NSF) awarded a $180,000 Project Grant to the University of Southern California (USC) Department of Contracts and Grants Division under the Mathematical and Physical Sciences (CFDA 47.049) program. The 3-year grant will support research on "Combinatorial Representation Theory of Quantum Groups and Coinvariant Algebras." The project aims to further develop combinatorial diagrams called "web bases" that encode the representation category of quantum groups, enabling efficient computations with powerful topological quantum invariants. This work connects diverse topics including total positivity, alternating sign matrices, plane partitions, crystal bases, and the geometry of the affine Grassmannian. USC will involve students in this research project, which is expected to provide concrete opportunities for them to develop problem-solving, software development, and other key skills. The award reflects NSF's mission to advance scientific knowledge and strengthen U.S. leadership in mathematics and related STEM fields.
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