Sergio Cristancho (Princeton) - Inequalities for metric trees and matroids

Abstract: The remarkable connection between metric trees and matroids was first observed by Sturmfels and Speyer in their study of the tropical Grassmannian. Since then, Brändén and Huh bridged this connection to the theory of Lorentzian polynomials. Classical results on the spectra of the distance matrices of metric trees both by Graham and Pollack, and Schoenberg serve as a fundamental ingredient for the latter. In this talk I want to share upcoming joint work with Ardila, Denham, Eur, Huh and Wang, where we (1) expand on the classical study of tree distance matrices in order to (2) obtain novel log-concavity inequalities that generalize Mason's conjecture for matroids, answering questions posed by Pak, and Giansiracusa, Rincón, Schleis and Ulirsch.