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. | |
Functional analysis, harmonic analysis, geometric analysis, elliptic and parabolic PDEs, variational calculus. | Yann.Bernard@monash.edu | |
| 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 Howie | Topology of 3-manifolds | josh.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 Popiel | Finite 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 Ibarra | Low-dimensional topology, geometry, knot theory, hyperbolic Dehn surgery and 3-manifolds. | Dionne.Ibarra@monash.edu |
| Dr Melissa Lee | Finite group theory, representation theory of simple (and related) groups, group actions on discrete structures. | Melissa.Lee@monash.edu |