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Explore the connections between quivers, 3D gauge theories, and three-manifolds in this 40-minute lecture by Shi Cheng from Fudan University. Delve into the ongoing research aimed at developing an intuitive physical and geometric interpretation of the knots-quivers correspondence. Examine the progress made in understanding the relationships between quivers encoding DT-invariants, 3D N=2 gauge theories with matter, and three-manifolds with Ooguri-Vafa defects. Discover how equivalent quivers relate to Seiberg dualities and Kirby moves, and gain insights into the dictionary linking quivers, gauge theories, and geometries in this advanced physics presentation from the Banach Center.