Project Grant 2205962

This Project Grant from the National Science Foundation Division of Mathematical Sciences provides $194,902 to Texas A&M University under the Mathematical and Physical Sciences program (CFDA 47.049) to study the quantum symmetries of topological phases of matter. The investigator will classify and distinguish topological phases through their mathematical symmetries, probe their properties, and understand relationships between phases through transitions. Some emphasis will be placed on potential applications in quantum technologies. Theoretical and computational methods will be employed to model topological phases of matter, with a focus on two-dimensional systems and developing understanding of three-dimensional systems and their representations. Key areas of investigation include braided fusion categories modeling topologically invariant features, and motion group representations encoding topological dynamics. Insights gained will further the understanding of the landscape of topological phases of matter. The three-year award period began September 1, 2022.