Moduli of relations of quivers

The derived category of coherent sheaves on an algebraic variety admitting a tilting object is described in terms of a quiver with relations, and one can study not necessarily commutative deformations of the variety by deforming the relations. In the talk, we will discuss our joint work with Tarig Abdelgadir and Shinnosuke Okawa on moduli spaces of relations of quivers associated with the projective plane, the quadric surface, and cubic surfaces.