# Chris McDaniel: Higher Lorentzian Polynomials, Higher Hessians, and Hodge-Riemann Relations for (codimension two) graded Artinian Gorenstein algebras

**Time: **
Mon 2023-03-27 15.00 - 16.00

**Location: **
Zoom

**Video link: **
Meeting ID: 637 0297 3803

**Participating: **
Chris McDaniel, Endicott College

**Abstract.**

In their seminal paper, P. Bränden and J. Huh have introduced a remarkable family of homogeneous polynomials called Lorentzian polynomials that provides a concrete connection between the Hodge-Riemann relations in degree one (an algebraic condition motivated inspired by Kähler geometry) and log concavity (a combinatorial condition). In this talk, we focus on the two variable case, and introduce the family of higher Lorentzian polynomials which provide a connection between Hodge-Riemann relations in higher degree and a notion of higher log concavity related to total positivity. Open problems will be given at the end.