Abstract: 
We discuss the asymptotics and the spectral monodromy of the quasi-exactly solvable part of the spectrum of the quasi-exactly solvable quartic.
We formulate a conjecture on the coincidence of the asymptotic shape of the level crossings of the latter oscillator
with the asymptotic shape of zeros of the Yablonskii-Vorob'ev polynomials.
Jointly with B. Shapiro.