Jacob Matherne: Examples of Lorentzian polynomials

Abstract:

Lorentzian polynomials were introduced by Brändén and Huh in 2019. They are a generalization of homogeneous stable polynomials, and they have recently been used to prove log-concavity properties for a number of interesting polynomials in a variety of areas of mathematics.

The purpose of this talk is to share some families of polynomials that are either known or expected to be Lorentzian, especially from the areas of algebraic combinatorics and representation theory. Two important classes I will focus on are the (normalizations of) Schur polynomials and the chromatic symmetric functions of certain graphs appearing in the study of Hessenberg varieties. The talk will be based on joint work with June Huh, Karola Mészáros, Alejandro Morales, Jesse Selover, and Avery St. Dizier.