Pure Mathematics

Pure mathematicians deal with the ideal, the beauty of perfection. They imagine the unimaginable. And magically, such constructions become the basis for applied mathematics to solve the most concrete problems. Research strengths include analysis, discrete mathematics, geometry and topology.

Research groups

Academic Staff

Dr Santiago Barrera Acevedo

Algebraic design theory, cocyclic Hadamard matrices, relative difference sets, correlation of finite arrays, and other combinatorial designs.


Dr Yann Bernard

Functional analysis, harmonic analysis, geometric analysis, elliptic and parabolic PDEs, variational calculus.

Dr Julie Clutterbuck

Eigenvalues, parabolic equations, heat flow, geometric analysis, calculus of variations, geometric evolution equations, mean curvature flow.


Prof Heiko Dietrich Computational algebra, in particular, group theory, Lie theory, and some aspects of algebraic design theory. Heiko.Dietrich@monash.edu
A/Prof Norman Do Geometry, topology, combinatorics and mathematical physics, enumerative geometry, moduli spaces of curves, Gromov-Witten theory, graphs on surfaces, matrix models and topological recursion. Norm.Do@monash.edu
Prof Jerome Droniou Numerical methods for elliptic and parabolic PDEs, polytopal meshes, high-order methods, finite volume methods, convergence analysis, compactness techniques. Jerome.Droniou@monash.edu
A/Prof Zihua Guo Harmonic/Fourier analysis, nonlinear PDEs of dispersive type and Fluid dynamics. Zihua.Guo@monash.edu
Dr Andy Hammerlindl Dynamical systems and ergodic theory.  Interactions between geometry, topology, and dynamics. Andy.Hammerlindl@monash.edu
Dr Jian He Topology and geometry, symplectic and contact geometry, holomorphic curves, low dimensional topology. Jian.He@monash.edu
A/Prof Daniel Horsley Combinatorial designs and edge decompositions of graphs, especially embedding, colouring and matching problems for block designs and cycle decompositions of graphs. Daniel.Horsley@monash.edu
Dr Josh HowieTopology of 3-manifoldsjosh.howie@monash.edu
Dr Mikhail Isaev Analytic methods in enumerative combinatorics, generating functions, asymptotic analysis, random graphs and hypergraphs. Mikhail.Isaev@monash.edu
Dr Daniel Jackson Mathematical physics, differential geometry, efficient numerical solution of ordinary and partial differential equations. daniel.jackson@monash.edu
Dr Ngan Le Theoretical and numerical analysis of stochastic partial differential equations, anomalous sub-diffusion equations. Ngan.Le@monash.edu
A/Prof Daniel Mathews Low-dimensional topology, knot theory, contact and symplectic topology, hyperbolic geometry, Heegaard Floer homology, mathematical physics, topological quantum field theory, and their algebraic, geometry, and combinatorics. Daniel.Mathews@monash.edu
Prof Todd Oliynyk Partial differential equations, singular limits of symmetric hyperbolic systems, geometric PDEs, general relativity, Newtonian limit, post-Newtonian expansions, Einstein-Yang-Mills, gravitating perfect fluids and elastic bodies, geometric flows, Ricci flows, renormalization group flow. Todd.Oliynyk@monash.edu
Dr Judy-anne Osborn judy-anne.osborn@monash.edu
Prof Burkard Polster Finite and topological geometry, combinatorial designs, group theory, history of mathematics, classical interpolation theory, computer visualisation, mathematics education and outreach. Burkard.Polster@monash.edu
Dr Tomasz PopielFinite group theory, finite incidence geometry, algebraic geometry over finite fields.Tomasz.Popiel@monash.edu
Prof Jessica Purcell Low-dimensional topology and geometry.


Dr Wenhui Shi Nonlinear Partial Differential Equations, calculus of variations. Wenhui.Shi@monash.edu
Dr Michelle Strumila Algebraic topology, higher category theory, Topological Quantum Field Theories and generalised infinity operads. michelle.strumila@monash.edu
Mr Simon Teague Simon.Teague@monash.edu
Prof Warwick Tucker Dynamical systems, Chaos theory, Computer-assisted proofs, Artificial intelligence. Warwick.Tucker@monash.edu
Prof Ian Wanless Latin squares and other combinatorial matrices; quasigroups, matrix permanents, graph theory (matchings, factorisations, random graphs), enumeration algorithms for combinatorial objects. Ian.Wanless@monash.edu
Prof David Wood Discrete mathematics and theoretical computer science, with an emphasis on structural graph theory, geometric graph theory, graph colouring, graph drawing, and combinatorial geometry. David.Wood@monash.edu
Prof Nick Wormald  Random structures and probabilistic combinatorics, graph theory, enumeration of graphs and maps, asymptotic enumeration and minimal Steiner trees. Solving combinatorial problems using real and complex analysis, probability and stochastic processes, and generating functions. Nick.Wormald@monash.edu

Research Fellows

Dr Dionne IbarraLow-dimensional topology, geometry, knot theory, hyperbolic Dehn surgery and 3-manifolds.Dionne.Ibarra@monash.edu
Dr Melissa LeeFinite group theory, representation theory of simple (and related) groups, group actions on discrete structures.Melissa.Lee@monash.edu