On polynomial families satisfying linear ODE or finite recurrence relations

In this talk we discuss several classes of families of polynomials in one complex variable, which are either (i) polynomial solutions to a linear ordinary differential equation depending on a spectral parameter, or (ii) satisfy a finite recurrence relation with fixed polynomial coefficients. In both cases, we describe some intriguing properties of the asymptotic distributions of zeroes and formulate a number of conjectures relating this topic to the study of Stokes curves. No preliminary knowledge of the subject is required.