Abstract: This is joint work with Daniel Chan (UNSW Sydney). Moduli spaces are a fruitful way of studying a given abelian category, take for example the moduli of point-like objects in non-commutative projective spaces or the moduli of representations of the McKay quiver. These examples yield moduli varieties, elliptic curves and minimal resolutions of Kleinian singularities respectively. Sometimes, however, the problem lends itself better to algebraic stacks as in the case of Ringel's canoncial algebras and weighted projective lines. We will start with a stack and a direct sum of line bundles that form a tilting bundle and recover the stack from the corresponding category of quiver representations.

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