3-Calabi-Yau algebras and non-commutative DT invariants

Sergey Mozgovoy

A bipartite graph on a torus, called a brane tiling by physicists, gives rise to a quiver with a potential. We discuss the corresponding quiver potential algebra, which is a 3-Calabi-Yau algebra under certain consistency conditions on a brane tiling. We also discuss the Donaldson-Thomas type invariants of the moduli spaces of framed modules over this algebra. It turns out that these invariants are closely related to the perfect matchings of the periodic bipartite graph on the universal cover of the torus.