  Given a brane tiling, that is, a bipartite graph on a torus, we can associate
with it a singular 3-Calabi-Yau variety. Using the brane tiling, we can also
construct all crepant resolutions of the above variety. We give an explicit
toric description of tilting bundles on these crepant resolutions. This result
proves the conjecture of Hanany, Herzog and Vegh and a version of the
conjecture of Aspinwall.
