Reconstruction of Modular Data from Representations of SL(2,Z)

Learn about modular data reconstruction from SL(2,Z) representations in this academic seminar talk delivered by Professor Siu-Hung Ng from Louisiana State University at the BIMSA-Tsinghua Quantum Symmetry Seminar. Explore how modular data, a crucial invariant of modular tensor categories, connects to families of projectively equivalent linear representations of SL(2,Z). Discover the groundbreaking research showing that 6-dimensional congruence SL(2,Z) representations are either unrealizable or derived from Galois conjugates of quantum group modular tensor categories' modular data. Follow along as Professor Ng, a distinguished researcher and 2019 Alexanderson Award recipient known for his work on Hopf algebras and tensor categories, presents joint findings with Eric Rowell, Zhenghan Wang, and Xiao-Gang Wen, demonstrating how this reconstruction process can be automated for higher-dimensional representations.