Realizing Modular Data from Centers of Near-Group Categories

This lecture from the BIMSA-Tsinghua Quantum Symmetry Seminar features Dr. Qing Zhang from the University of California, Santa Barbara discussing the modular data arising from Drinfeld centers of near-group categories. Explore how modular data can be computed by solving Izumi's polynomial equations, focusing on a near-group category of type Z/4Z × Z/4Z + 16. Learn about obtaining rank 10 modular data through condensation and its alternative realization via the Drinfeld center of a rank 4 fusion category. Discover connections between the modular data of a Z/8Z + 8 near-group category's Drinfeld center and the quantum group category C(g₂, 4). The presentation is based on joint work with Zhiqiang Yu and includes detailed mathematical analysis with accompanying slides available online. Dr. Zhang, a Visiting Assistant Professor at UCSB whose research focuses on tensor categories, delivers this 71-minute technical talk aimed at researchers in quantum symmetry and category theory.