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Explore the intricate world of knot theory in this 56-minute lecture by Wei Li from the Chinese Academy of Sciences, presented at the Banach Center. Delve into quiver Yangian algebras and their representations for various quivers and potentials. Discover the fascinating connections between these algebraic structures and knots through the knot-quiver correspondence. Examine a novel gluing construction for certain algebras and its relationship to knots, independent of quiver representations. Gain insights into advanced mathematical concepts at the intersection of algebra and topology in this comprehensive exploration of algebras for knots.