Higher algebraic and categorical structures from two-dimensional conformal field theory

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The study of two-dimensional conformal field theories has rich interactions with the developments of higher representation and higher category theories. We propose to study some topics arising from recent developments in 2d CFT that not only are interesting in their own right but also help to provide insights into the general theory: (a) Higher monoidal categories and higher braidings (b) Generalized string-net constructions and derived modular functors (c) Cylinder categories, categorified traces, and topological cyclic homology of bicategories