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Explore advanced concepts in fusion categories through this 52-minute conference lecture delivered by J. Plavnik from Indiana University as part of the 2025 SCGCS School on Topological Symmetries and Defects in Quantum Field Theory. Delve into the latest theoretical developments and mathematical frameworks that govern fusion categories, building upon foundational knowledge to examine cutting-edge research in this specialized area of mathematical physics. Gain insights into the intricate relationships between topological symmetries and defects in quantum field theory through the lens of categorical structures, with particular emphasis on recent breakthroughs and emerging methodologies in the field. This second part of the lecture series provides detailed analysis of advanced topics, offering participants a comprehensive understanding of how fusion categories contribute to our understanding of quantum field theoretical phenomena and their topological properties.
