Arnold's seminar, Moscow University, March 20, 2001

B.Shapiro (Univ. of Stockholm)

   'New results and conjectures on the polynomial eigenfuctions to
    d^k/dx^k (Qf) where Q is a degree k polynomial'

In this talk we continue discussing a number of conjecture related to the
behavior of the zero sets of the polynomial eigenfunctions to d^k/dx^k (Qf).
A number of quite surprising properties were earlier observed in the numerical
experiments by G.Masson and B.Shapiro (the article is on the seminar's
homepage). Recently some of them were rigorously proved by H. Rullgaard
and H.Shapiro (none of the Shapiros you probably know). I will report on
this recent progress and add some more cream.