Algebraic Combinatorics Seminar - David Wagner

Title: Some new lemmas about polynomials with only real roots

Abstract:

Recent investigations in Ehrhart theory suggested some conjectures involving interlacing relations among polynomials with only real roots, and Veronese sections of them. Revisiting some old theorems, we find as corollaries some new lemmas which have been overlooked for a long time. One of these lemmas directly implies a strong form of the motivating conjecture.  Similar applications of the other lemmas are anticipated. This is ongoing joint work with Christos Athanasiadis (U. Athens).