Student Colloquium

James Haley, Department of Pure Mathematics, University of Waterloo

“Preserving Reality”

We can construct linear operators acting on polynomials that take polynomials with only real zeros to polynomials with only real zeros. By varying the basis for the polynomials for which these operators are defined, we can obtain various classes of these operators which turn out to be nested. Because these operators are unbounded, operator theory in the sense that it is studied at Waterloo does not generally apply.

M3-3103