On non-Abelian monodromy surfaces of the Painleve equations

Due to the isomonodromic property, the space of solutions of the Painleve equations can be parameterized by the monodromy data. Namely, each of the equations can be associated with an affine cubic that is usually called the monodromy surface. Various examples of non-abelian analogs of the Painleve equations have arisen in recent years. In this talk we will discuss how to derive a non-commutative analog of the monodromy surface for them. We will consider the second Painleve equation as an example.