Phylogenetic combinatorics is a new branch of applied mathematics concerned with the combinatorial description and analysis of evolutionary trees and related structures such as split systems, metrics and phylogenetic networks. It represents a unifying framework to handle the combinatorial structures that commonly appear in evolutionary studies, and has provided useful computational tools and algorithms for evolutionary analysis. In this project, Huber and Moulton will visit Prof. Allen Rodrigo to explore new applications of phylogenetic combinatorics to some cutting-edge problems in evolution.