Representation Theory of Extended Operators - Tannaka Duality and Koszul Duality in QFT, Part 4

Explore advanced representation theory concepts in quantum field theory through this lecture focusing on Tannaka duality and Koszul duality as applied to extended operators. 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 about the categorical aspects of representation theory in the context of extended operators, with particular emphasis on how Tannaka reconstruction relates physical symmetries to their mathematical representations. Investigate the role of Koszul duality in organizing the algebraic structures that emerge in quantum field theories with topological features. Gain insights into how these sophisticated mathematical tools illuminate the deep connections between algebra, topology, and physics in modern theoretical frameworks. This presentation forms part of a comprehensive series on topological symmetries and defects, building upon previous discussions to develop a complete picture of how extended operators function within quantum field theoretical contexts.