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Explore the intricacies of 3-dimensional Homotopy Quantum Field Theories (HQFTs) in this comprehensive 57-minute lecture delivered by Alexis Virelizier. Delve into the mathematical foundations and applications of HQFTs within the realm of quantum topology. Gain insights into the connections between quantum field theory and algebraic topology, and discover how these theories contribute to our understanding of three-dimensional manifolds and their invariants. Examine the key concepts, techniques, and recent developments in this fascinating area of mathematical physics, as presented by an expert in the field.