On the scalar approach to the weak asymptotics problem for $\mathcal{GN}$-systems

The talk will be devoted to recent achievements in the problem of extending the new approach to describe the weak asymptotics of Hermite–Pade polynomials to a wider class of $\mathcal{GN}$-systems. This approach was suggested by S. Suetin in 2018 and is based on the use of the scalar equilibrium problem on a compact Riemann surface with an external harmonic field. I will also discuss equivalence of the corresponding method with the classical vector potential technique.