Pure mathematics research underpins the tools and techniques that applied mathematicians, scientists and engineers use to find solutions to realworld problems.
Our research group brings together an internationally recognised team of pure mathematicians with a diverse skill set. By fostering a highly collaborative style of working and combining our individual strengths, we are able to produce extraordinary results.
The expertise of the Pure Mathematics group covers:


Research focus  Investigators  Funding 
Finite linearly representable geometries and symmetry  Cheryl Praeger  ARC Discovery Project 
Real chromatic roots of graphs and matroids  Gordon Royle  ARC Discovery Project 
Permutation groups and their interrelationship with the symmetry of graphs codes and geometric configurations  John Bamberg Alice Devillers Cheryl Praeger  ARC Discovery Project 
Cayley graphs and their associated geometric and combinatorial objects  CaiHeng Li John Bamberg  ARC Discovery Project 
Finite geometry from an algebraic point of view  John Bamberg  ARC Future Fellowship 
Harnessing symmetry to advance the study of graphs  Michael Giudici  ARC Discovery Project 
Efficient computation in finite groups with applications in algebra and graph theory  CaiHeng Li  ARC Discovery Project 
Permutation groups with finite subdegrees and the structure of totally disconnected locally compact groups  Simon Smith  ARC Discovery Early Career Researcher Awards 
Enumeration of vertextransitive graphs  Gabriel Verret  ARC Discovery Early Career Researcher Awards 
Researcher  Expertise  
John Bamberg  Finite geometry, group actions  
Alice Devillers  Buildings, permutation groups, graph symmetry  
Joanna Fawcett  Permutation groups  
Stephen Glasby  Group theory, computation  
Michael Giudici  Permutation groups, algebraic graph theory, finite geometry  
Cai Heng Li  Group theory, graph symmetry, and surface embeddings  
Luke Morgan  Group theory, graph symmetry  
Binzhou Xia  Group theory, graph symmetry  
Irene Pivotto  Graph theory, matroid theory  
Tomasz Popiel  Computational group theory, finite geometry, differential geometry  
Cheryl Praeger  Permutation groups, graph symmetry and designs, computation  
Gordon Royle  Graph theory, matroid theory  
ShuJiao Song  Permutation groups, graph symmetry  
With ten externally funded researchonly staff members, the Pure Mathematics research group has an exceptional trackrecord in postdoctoral training in pure mathematics within Australia and internationally.
The wide range of expertise covered by our group provides outstanding opportunities for postgraduate projects in areas such as algebra, discrete mathematics, analysis and geometry.
Recently, our postgraduates have studied the following topics: