The Algebra & Topology research program explores the areas of algebraic geometry, representation theory, algebraic topology, K-theory, analytic number theory, operator algebras, low-dimensional and symplectic topology, and homological algebra.

The Analysis & Geometry research program explores the areas of differential geometry, several complex variables, non-commutative geometry, harmonic analysis, microlocal analysis, partial differential equations, operator theory, spectral theory, convex geometry and statistical learning theory, and banach algebras.

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.

research researchers backgrounds mathematics, statistics quantitative biology goal developing new techniques analysing complex biological systems.

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

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.