Speaker
Description
Traditionally, weak asymptotics of Hermite--Padé polynomials for various systems of Markov functions (such as the Angelesco and Nikishin systems) is described in terms of the vector potential problem on the complex plane. This approach has a number of limitations in context of generalisation of Stahl’s theory on Hermite--Padé polynomials. Development of the alternative language was initiated by Sergey Suetin
(Steklov Institute, Moscow) in 2018. He considered a very special generalised Nikishin system ($\mathcal{GN}$ system) of two functions; corresponding weak asymptotic problem was solved via scalar potential problem with a harmonic exterior field on a Riemann surface of genus zero. This technique was generalised on the slightly wider class of $\mathcal{GN}$ systems by me in 2021; the corresponding potential problem lives on a Riemann surface on genus $g>0$. In this talk I will summarise recent results on the development of this scalar approach.
