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Explore a mathematical seminar presentation that delves into proving how the motive of the stack of sheaves on a stacky curve is generated by the motive of the curve's coarse space. Examine the intricate relationship between torsion sheaves on stacky curves and representations of cyclic quivers, with particular attention to the underlying geometric constructions central to the proof. Learn about the potential connections to a graded version of the Grothendieck-Springer resolution in this 52-minute lecture delivered at the Isaac Newton Institute as part of the New Equivariant Methods in Algebraic and Differential Geometry program.