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Explore an advanced mathematics lecture on local modules in braided fusion 2-categories, delivered by Hao Xu from Georg-August-Universität Göttingen at the BIMSA-Tsinghua Quantum Symmetry Seminar. Delve into the intricate relationship between braided algebras and their modules in braided fusion 2-categories, examining how local modules over separable braided algebras form braided multifusion 2-categories. Learn about the centralization properties between local and free modules, and discover the novel concept of reciprocity unique to the 2-categorical setting. Investigate Lagrangian algebras in braided fusion 2-categories and their crucial role in classifying topological boundaries of (3+1)D topological orders, with particular focus on the mathematical classification of bosonic fusion 2-categories through Lagrangian algebras in the Drinfeld center of strongly fusion 2-category $\mathbf{2Vect}^\pi_G$.
