Algebraic and enumerative combinatorics seminar-Graham Denham

Title: Distances in trees and inequalities for matroids

Abstract: The distance matrix of a tree appears in a range of contexts, from phylogenetics to physical chemistry.  I will describe a new result about the spectrum of this matrix, one that gives affirmative answers to two questions about matroid positivity properties.  These are both strengthenings of Mason's conjectures about the log-concavity of sequence of numbers of independent sets of a matroid, proposed byIgor Pak and by Giansiracusa, Rincón, Schleis, Ulirsch, respectively.

This is joint work with Federico Ardila, Sergio Cristancho,Chris Eur, June Huh, and Botong Wang.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.