Algebra & topology


We work on problems of central interest in mathematics. Our primary research areas include number theory, representation theory, low-dimensional topology, algebraic geometry, algebraic topology, homological algebra, geometric group theory, cluster algebras, and symplectic geometry. We also have strong ties with other parts of the Mathematical Sciences Institute, and we collaborate regularly with researchers in mathematical physics, geometry, and applied topology. In addition to the ongoing research of our continuing staff, we support undergraduate, honours, masters and PhD students. We also host a steady stream of postdoctoral and visiting scholars.


  • Vigleik Angeltveit: Algebraic Topology, stable homotopy theory, algebraic K-theory, Ramsey theory.
  • Asilata Bapat: Geometric representation theory, homological algebra.
  • Jim Borger: Number theory and algebraic geometry.
  • Anand Deopurkar: Algebraic geometry and its connections to number theory, representation theory, and mathematical physics. Homological algebra.
  • Ian Le: Representation theory and algebraic combinatorics. Cluster theory.
  • Joan Licata: Low-dimensional topology and contact geometry. Knot theory and Floer theoretic invariants.
  • Amnon Neeman: Algebraic K-theory, algebraic geometry, topology, homological algebra.
  • Uri Onn: Representation theory. Analytic and Algebraic groups.
  • Brett Parker: Symplectic geometry and Gromov-Witten and related invariants using exploded manifolds.
  • Adam Piggott: Geometric group theory. Rewriting systems, automorphisms of the free group.
  • James Tener: Operator algebras, functional analysis, and representation theory. Mathematical foundations of quantum field theory.
  • Katharine Turner: Computational topology. Topological data analysis.
  • Bryan Wang: Geometric properties of moduli spaces in symplectic topology. Gauge theory.

Reasons to work with us

We are one of the largest and broadest mathematical research groups at ANU. We support an active, collaborative research and learning environment. Our regular topics courses, seminars, and learning groups aimed at fostering interactions between mathematicians at all levels, from undergraduates through to continuing faculty. Our mathematicians are international leaders in their fields, and we maintain active collaborations with mathematicians all over the world.

Filter by keyword
Project Supervisors
Algebraic topology
Arithmetic algebraic geometry
Arithmetic and Geometry over Finite Fields
Combinatorial and Geometric Group Theory
Complex cobordism & stable homotopy
Computability in Algebra and Geometry
Crystallographic groups
Dirac operators and application
Enriched monoidal categories
Fermat's last theorem
Galois theory in topology
Geometry of Gauge fields
Group Actions and Invariants
Homological Algebra and Algebraic Geometry
Interactive and automated theorem proving
Kervaire invariant one problem
Mathematical Aspects of Conformal Field Theory
Model Categories
Model categories in algebraic topology
Morse theory in dimensions three and four
Number theory & algebraic geometry
Readings in Commutative Algebra and Algebraic Geometry
Reflection groups, cacti and crystals
Representation theory and combinatorics of symmetric groups
Riemann zeta function & the distribution of primes
Spectral Sequences in Algebraic Topology
Statistical shape analysis using algebraic topology
Surface mapping class groups
Topics in contact geometry
Topics in low-dimensional topology
Topics in representation theory
Topology of Singularities