Research topics in algebra include radical theory and ring theory; semigroups, varieties, e-varieties and pseudovarieties; coding and cryptography, finite automata, formal languages, data structures, rewriting systems and algorithms.

Research is conducted in pure analysis - measure theory, harmonic analysis and representation theory - as well as numerical analysis, approximation theory and integral equations.

Modern analytical techniques are being used to assess the environmental impact of anthropogenic activities on urban air and aquatic environments. Research includes studies into wood smoke pollution, inorganic contaminants in aquatic sediments and the use of sediment cores to establish historical profiles of contaminant levels. Methods to cleanup industrial and agricultural effluents are also under development, as are techniques for environmental sampling using biomarkers and passive samplers.

Active research topics include free-boundary problems in fluid mechanics; non-linear oscillations in chemical and mechanical systems; asymptotic and perturbation analysis; differential and integral equations; static magnets and gradient coils in magnetic resonance imaging (MRI) devices; meteorology; oceanography.

This project aims at understanding both the growth dynamics of Australian arrow squid, its trophic role in the marine ecosystem and information to better manage the fishery for Nototodarus gouldi in Australian waters.