Francesco Calogero: On the generations of monic polynomials obtained by replacing the coefficients of the polynomials of the next generation with the zeros of a polynomial of the previous generation

Generations of monic polynomials, all of arbitrary degree N, are obtained from a seed polynomial of degree N by identifying the coefficients of the polynomials of the next generation with the zeros of a polynomial of the previous generation; and Diophantine properties are reported of the zeros of the polynomials thereby obtained when the seed polynomial is the Hermite polynomial of degree N. This is joint work in progress with Oksana Bihun.