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Learn about reconstructing and discovering modular data from congruence representations of SL(2,Z) in this academic seminar talk from the BIMSA-Tsinghua Quantum Symmetry Series. Explore how modular fusion categories (MFCs) emerge across mathematics and physics, focusing on their crucial invariants known as modular data. Professor Siu-Hung Ng, an award-winning mathematician from Louisiana State University known for his work on Hopf algebra and tensor categories, explains the relationship between modular data and uncanonical congruence representations of SL(2,Z). Drawing from his research with collaborators Eric Rowell, Zhenghan Wang, and Xiao-Gang Wen, discover the mathematical techniques used to mine these important structural relationships. The presentation includes detailed slides covering the theoretical foundations and practical applications of this advanced mathematical concept in quantum symmetry research.
