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Explore the unexpected connections between the Deligne-Simpson problem and Hitchin systems in this 1-hour 6-minute lecture by Ron Donagi from the University of Pennsylvania. Delve into the intriguing world of products of matrices, non-Abelian Hodge theory, integrable systems, and theories of Class S. Gain insights into how these concepts are interrelated and motivated by work on SCF Theories of Class S and 3D mirror symmetry. Enhance your understanding of advanced mathematical concepts and their applications in theoretical physics.