I have a wide range of interests under the broad umbrella of applied dynamical systems; I have also worked in the area of mathematical ecology, specialising in mathematical models of animal behaviour and movement.
One of my main research areas is understanding the dynamics and structure of so-called heteroclinic networks. A heteroclinic network is an object in a differential equation which is often associated with intermittent behaviour: solutions of the differential equation will spend some time displaying a certain type of behaviour before rapidly switching to a different type of behaviour. Most of my research in this field until now has been rather theoretical, and I am in the process of shifting my focus to extend this research to use heteroclinic networks methods to both develop and understand models of physical systems. Heteroclinic networks arise naturally in mathematical models describing a diverse range of physical systems, including fluid dynamics, interactions between populations, cognitive systems and game theory.
Aside from research, I am also very concerned about the under-representation of women in the mathematical sciences, and at the University of Auckland, I co-founded the Undergraduate Women in Science Network. The aim of the network is to reduce the isolation reported by many undergraduate women and increase the visibility of senior women working in science.