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Explore advanced concepts in theoretical physics through this lecture that delves into non-invertible symmetries and dualities, building upon foundational principles established in previous sessions. Learn how these mathematical structures emerge in quantum field theory and condensed matter systems, with particular emphasis on their role in understanding phase transitions and topological phenomena. Examine the relationship between symmetry breaking, duality transformations, and their applications to modern problems in theoretical physics. Discover how non-invertible symmetries provide new tools for analyzing quantum many-body systems and their exotic phases of matter. Investigate the mathematical framework underlying these concepts and their connections to anomalies, topology, and quantum information theory. Gain insights into cutting-edge research directions where these symmetries play crucial roles in understanding emergent phenomena in condensed matter physics and quantum field theory.
