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Explore a 53-minute academic lecture from the BIMSA-Tsinghua Quantum Symmetry Seminar where Professor Jingcheng Dong from Nanjing University of Information Science and Technology presents groundbreaking research on modular categories. Delve into mathematical proofs demonstrating that modular categories of Frobenius-Perron dimension p²q²r²m are solvable, where p, q, and r represent distinct prime numbers, and m is square-free with gcd(m,pqr)=1. Learn about significant applications showing that integral modular categories of Frobenius-Perron dimension less than 1800 are solvable, leading to the conclusion that integral perfect modular categories must have Frobenius-Perron dimension greater than or equal to 1800. Examine additional findings related to weakly group-theoretical modular categories, with research conducted in collaboration with Dewei Zhou.
