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Explore the intricacies of state sum homotopy quantum field theories in this comprehensive lecture delivered by Alexis Virelizier at the Galileo Galilei Institute. Delve into advanced mathematical concepts and their applications in quantum field theory as Virelizier presents a detailed analysis of state sum approaches to homotopy QFTs. Gain insights into the latest developments in this field and understand how these theories contribute to our understanding of fundamental physics. Over the course of 77 minutes, examine the mathematical structures underlying these theories and their implications for both theoretical physics and mathematics.