amoeba, coamoeba and non-commutative Donaldson-Thomas invariants

I this talk I will discuss non-commutative Donaldson-Thomas invariants for a class of toric Calabi-Yau manifolds. The generating function of these invariants is computed by a crystal melting model, which is determined by the ``tropical limit'' of the coamoeba of the Newton polynomial of the toric diagram. In the thermodynamic limit, the limit shape of the crystal gives amoeba of the mirror Calabi-Yau manifold. If time allows, I will also discuss the wall crossing of Donaldson-Thomas invariants.