Daniel Qin: Some elementary results on symmetric Lorentzian Polynomials

Abstract.

In 2020, Huh-Matherne-Mészáros-St.Dizier proved that normalized Schur polynomials are Lorentzian and conjectured that other Schur-type symmetric polynomials are as well. More recently in 2022, Matherne-Morales-Selover proved that chromatic symmetric functions of indifference graphs of abelian Dyck paths are Lorentzian. Motivated by these results, we study the more general class of Lorentzian polynomials that are invariant under the standard permutation action on variables. In this talk, we give a few basic results on symmetric Lorentzian polynomials.