We work on problems of central interest in mathematics.

The Mathematical Analysis research group in MSI researches fundamental questions about functions and continuous processes.

Current research in the Applied & Nonlinear Analysis research program emphasises elliptic and parabolic partial differential equations, geometric and physical variational problems, geometric partial differential equations, geometric evolutions, geometric measure theory, optimal transportation, affine differential geometry, conformal differential geometry, finite element and difference equation approximations, and geometry of fractals.

Group expertise lies in biological mathematics and biostatistics, with current research areas focus on population genetics, phylogenetics, and spatial modelling

The Computational Mathematics research program actively studies theoretical aspects of computational algorithms.

The Plasma Theory and Modelling group focuses on understanding these fundamental properties of plasmas through a variety of different academic perspectives.

The Mathematics Physics research program spans the ANU College of Science, with several members having joint appointments with the Department of Theoretical Physics in RSPE. The program is active in studying fundamental problems across a broad spectrum of Mathematical Physics.

The Stochastic Analysis & Risk Modelling research program explores the areas of stochastic modelling of financial processes, statistical inference relating to those models, stochastic integration and numerical aspects of partial differential equations, and option pricing models.

The Theorectical Astrophysics research program explores the areas of compact stars, radiation processes and transfer mechanisms in accretion flows on to highly magnetic compact stars, modelling of accretion disks, modelling of stars and magnetic atmospheres, cataclysmic variable binaries, and searching for the progenitors of type Ia supernovae.