Research activity at MSI is focused into the following groups.

Algebra & topology »

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.

Analysis & geometry »

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.

Applied & nonlinear analysis »

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.

Bioinformation science »

The Bioinformation Science research program brings together researchers with backgrounds in mathematics, statistics and quantitative biology with the goal of developing new techniques for analysing complex biological systems.

Computational mathematics »

The Computational Mathematics research program actively studies theoretical aspects of computational algorithms, both in the continuous and discrete settings, as well addressing implementation issues to ensure efficient and reliable solution techniques.

Mathematical physics »

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.

Statistical science »

The Statistical Science research program explores the areas of statistical inference, statistical modelling, robustness, nonparametric and semiparametric methods, analysis of sample surveys, ecological monitoring, and applied work in ecology and chemistry.

Stochastic analysis & risk modelling »

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.

Theoretical astrophysics »

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.