Research areas
Research activity at MSI is structured into our research groups.
The Algebra & Number theory research area covers a broad range of fundamental topics in modern mathematics, including representation theory, homological algebra, cluster algebras, geometric group theory, algebraic number theory, algebraic combinatorics, and connections to algebraic geometry and combinatorics.
The Algebraic & Differential Geometry research area brings together expertise across geometry, algebra, and analysis to study fundamental questions in the areas of differential geometry, symplectic geometry, geometric partial differential equations, geometric evolutions, noncommutative geometry, algebraic geometry, number theory, and mathematical physics.
The Analysis & PDE research area covers a breadth of topics, including harmonic analysis, microlocal analysis, geometric and physical variational problems, elliptic and parabolic partial differential equations, dispersive equations, geometric partial differential equations, geometric evolutions, operator algebras, among other related research topics.
The Applied & Computational Mathematics research area studies a range of applied mathematical topics, including theoretical aspects of computational algorithms, computational PDEs, inverse problems, numerical linear algebra, computational topology, optimisation, data science, environmental science, mathematical modelling, theoretical plasma physics, and theoretical astrophysics.
Group expertise lies in biological mathematics and biostatistics, with current research areas focus on population genetics, phylogenetics, and spatial modelling.
The research area in Environnmental Mathematical Modelling covers a range of environmental issues, primarily water related. This includes hydrological and hydrodynamic modelling of flows and waves, statistical analysis of extreme events, and transdisciplinary research on flood impacts and water resources.
The Plasma Theory and Modelling group focuses on understanding these fundamental properties of plasmas through a variety of different academic perspectives.
The mathematical data science research area is focused in the ANU Mathematical Data Science Centre (MDSC). The MDSC was created to be a global leader in the development of the mathematical theory of data science, and to train the next generation of mathematical data scientists.
The Mathematics Physics research area encompasses applications to physics arising from diverse areas of mathematics. This includes applications to areas of physics such as string theory, quantum and conformal field theory, integrable models, and gauge theory using and developing techniques from across broad areas of algebra, analysis, and geometry.
The research area in Pure and Applied Topology covers includes algebraic topology, low-dimensional topology, the theory of knots and braids, homological algebra, contact geometry, and computational topology, as well as their applications in topological data analysis and mathematical physics.