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Explore advanced concepts in representation theory of extended operators through the lens of Tannaka duality and Koszul duality as they apply to quantum field theory in this second part of a specialized lecture series. Delve into the mathematical frameworks that connect algebraic structures with topological quantum field theories, examining how these dualities provide powerful tools for understanding symmetries and defects. Learn from T. Dimofte of the University of Edinburgh as he presents sophisticated theoretical constructions that bridge abstract algebra and modern physics, focusing on the categorical aspects of extended operators and their representations. Gain insights into how these mathematical concepts illuminate the structure of quantum field theories with topological features, building upon foundational material from the first part of this lecture sequence delivered at the 2025 SCGCS School on Topological Symmetries and Defects in Quantum Field Theory.
