Research Interests
 Integrable systems
 Mathematical Physics
 Enumerative combinatorics
 Statistical Mechanics
Research Groups
Extra Information
I hold the position of Professor in Mathematics and Statistics of the University. I conduct research in the area of phase transitions and critical phenomena in statistical mechanics especially pertaining to model polymer systems, which lies within the discipline of mathematical physics. This work endeavours to uncover the universal geometric and topological features of long chain molecules, such as DNA, in a variety of generic conditions. The models I study arise naturally in "Discrete Mathematics and Combinatorics" and in "Stochastic Processes". I am part of a 'Mathematical Physics and Statistical Mechanics Group' working on these topics.
I have several projects in the general area of the statistical mechanics of lattice polymer and vesicle models where there is scope for Master of Science and PhD projects, and some where postdoctoral collaboration would be fruitful. Please contact me if you are interested. The two main topics of interest are (1) numerical analysis, both Monte Carlo computer simulation and also exact enumeration techniques, of lattice walks, and (2) the exact solution of interacting directed walk systems.
Current Postgraduate Supervision
Name 
Thesis title 
Ruijie XU 

Past Postgraduate Supervision
Name 
Thesis title 
Debra BENNETTWOOD 
"Numerical studies of Selfavoiding walks" 
Eduardo DAGROSA 
"Statistical Mechanics of twiststoring polymers" 
Paul FIJN 
"The combinatorics and graph theory of stochastic interface and lattice path problems" 
Will JAMES 
"The enumeration of heaps and almostconvex polygons" 
Heather LONSDALE 
"Compact directed percolation near a damp wall" 
Paul NIDRAS 
"Critical behaviour of geometric cluster models" 
Judyanne OSBORN 
"Combinatorics of pavings and paths" 
Andrew RECHNITZER 
"Some problems in the counting of lattice animals, polyominoes, polygons and walks" 
Rami TABBARA 
"Generalised directed walker models of adsorption and gelation" 
Henry (Ling Heng) WONG 
"Topics on Lattice Models in Statistical Mechanics" 
Past MSc Students
Name 
Project title 
Andrew OPPENHEIM 
"Directed walkers on the square and triangular planar lattices" 
Andrew RECHNITZER 
"An investigation of Directed Percolation" 
Rami TABBARA 

Recent Grant History
Year(s) 
Source 
Type 
Title 
2016  2018 
ARC 
Discovery 
Interplay of Topology and Geometry in Polymeric Critical Phenomena 
2012  2014 
ARC 
Discovery 
Advanced numerical and analytical techniques for exact studies in combinatorics and statistical mechanics 
2007  2011 
ARC 
Discovery 
Searching for solvability in Statistical Mechanics and beyond using advanced Enumerative Combinatorics 
2004  2008 
ARC 
Network 
Complex Open Systems Network (COSNet) 
2003  2010 
ARC 
Centre Of Excellence 
ARC Centre of Excellence for Mathematics and Statistics of Complex Systems 
Responsibilities
 Academic Board member
 Associate Deans Learning and Teaching Forum
 Bachelors of BioMed/BSc Standing Committee member
 CEBRA Board
 Chair of Management Committee
 Chair of Strategic Planning Committee
 Deputy Dean
 Faculty Planning & Resources Committee member
 Lecture & 2nd Examiner Schedules
 MGSS Academic Programs Commitee
 MGSS Management Committee
 Research Support Scheme Committee member (RSS)
 Teaching & Learning Support
Committees
 Strategic Planning Committee