Soft Riemann–Hilbert problems and planar orthogonal polynomials

Riemann–Hilbert problems are jump problems where we look for an analytic function with a given jump along an interface.
I will discuss problems which are two-dimensional, and in fact there is no given interface, but instead a $\bar\partial$-problem. The interface only emerges in the limit and is the result of potential theory considerations. A much simplified approach which is based on the idea of a given algebraic form of the solution to the $\bar\partial$-problem is presented.