Explore a 58-minute lecture from the BIMSA-Tsinghua Quantum Symmetry Seminar where Bin Gui, Assistant Professor at Yau Mathematical Sciences Center of Tsinghua University, delves into the correspondence between twisted and untwisted theories in permutation orbifold conformal field theory. Learn how orbifold CFT operates with finite automorphism groups acting on vertex operator algebras, focusing on the case where symmetric group Sn acts by permutation on tensor products. Discover how twisted modules and their conformal blocks can be constructed from untwisted ones and vice versa in specific cases. Gain insights from Gui's extensive research background in vertex operator algebras, functional analysis, operator algebras, and tensor categories, including his groundbreaking work on unitarity in VOA representation categories and their equivalence with conformal nets representation categories.