University of Canterbury, NZ

Phylogenetics is the reconstruction and analysis of 'evolutionary'

trees and graphs in biology (and related areas of classification, such as linguistics). Discrete mathematics plays an important role in the underlying theory. We will describe some of the ways in which concepts from combinatorics (e.g. poset theory, greedoids, cyclic permutations, Menger's theorem, closure operators, chordal graphs) play a central role. As well as providing an overview, we also describe some recent and new results, and outline some open problems.

A central task in conservation biology is measuring, predicting, and preserving biological diversity as species face extinction. Dating back to 1992, phylogenetic diversity is a prominent notion for measuring the biodiversity of a collection of species. This talk gives a flavour of some the combinatorial and algorithmic problems and recent solutions associated with computing this measure. This is joint work with Magnus Bordewich (Durham University, UK) and Andreas Spillner (University of East Anglia, UK).