My primary area of expertise is the use of computational techniques for solving differential equations and studying interacting random walk models. Using computation, together with a range of techniques from applied mathematics, I study several physical and biological processes. Previous research has involved studying flow and transport processes in porous media, salt water intrusion, the design and analysis of efficient methods for solving reaction diffusion equations and the implementation of high performance shock capturing schemes to study chemotactic travelling waves.
More recent research interests include the study of collective cell migration, adhesive cell migration, moment dynamics models of cell population behaviour and lattice free random walk models. Studying problems from a wide range of fields has given me the opportunity to interact with several collaborators including applied mathematicians, statisticians, experimental cell biologists and civil engineers.
During 2019-2021, I am Deputy Director of the Australian Mathematical Sciences Institute. During 2016-2018 I am a member of the Australian Research Council's College of Experts, sitting on the Mathematics, Physics, Chemistry and Earth Sciences panel.I am also a member of the editorial board of PLOS ONE, the Journal for Engineering Mathematics and the ANZIAM Journal. Previously I have co-edited special issues of the Bulletin of Mathematical Biology and the ANZIAM Journal.
My most recent teaching interests include first year calculus and analysis, and later year courses on differential equations and applied mathematical modelling.