Non-commutative crepant resolutions and their DT invariants

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The purpose of this project is a detailed investigation of the non-commutative crepant resolutions of the toric Calabi-Yau threefolds associated to the brane tilings (bipartite graphs on a torus). These crepant resolutions are quiver potential algebras canonically determined by the brane tiling. We will investigate their Donaldson-Thomas type invariants and their relation to the Donaldson-Thomas invariants of the crepant resolutions. We will investigate if the mutations of this quiver potential algebra can be again represented as quiver potential algebras associated to some brane tilings. We will study exceptional collections in the derived category of the quiver potential algebra.