Lorentzian Polynomials · Notes for directed study

Proof of Theorem 2.23 (continued)

This week's event is hosted by Ivy Liu.

Overall Goal

The main objective across these two talks is to prove that the set \(L_n^d\) is closed, which, combined with the previous theorem presented by Marcus, ultimately proves that the closure of the strictly Lorentzian polynomials \(\mathring{L}_n^d\) is exactly \(L_n^d\).

General content

Today, we continue with the second part of the framework. To offer a slightly different perspective from the paper, I will introduce a modified concept, \(M^\#\)-convexity, motivated by the independent sets of matroids, which I believe provides a stronger intuition for the proof. We will then walk through an elegant minimal counterexample argument to establish the \(M\)-convexity.