Ext. Number:
  • Integrable systems
  • Mathematical Physics
  • Enumerative combinatorics
  • Statistical Mechanics
Recent Publications:
  • Self-attracting polymers in two dimensions with three low-temperature phases (2017) more
  • An exact solution of three interacting friendly walks in the bulk (2016) more
  • Winding angle distributions for two-dimensional collapsing polymers (2016) more
  • The role of three-body interactions in two-dimensional polymer collapse (2016) more
  • A semi-flexible attracting-segment model of three-dimensional polymer collapse (2015) more

Selected Publications

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 post-doctoral 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:
Past Postgraduate Supervision:
Debra N. BENNETT-WOOD "Numerical studies of Self-avoiding walks"
Eduardo DAGROSA "Statistical Mechanics of twist-storing polymers"
Paul FIJN "The combinatorics and graph theory of stochastic interface and lattice path problems"
Will JAMES "The enumeration of heaps and almost-convex polygons"
Heather LONSDALE "Compact directed percolation near a damp wall"
Paul NIDRAS "Critical behaviour of geometric cluster models"
Judy-anne 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:
Andrew RECHNITZER "An investigation of Directed Percolation"
Andrew OPPENHEIM "Directed walkers on the square and triangular planar lattices"
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
2003 - 2010 ARC Centre Of Excellence ARC Centre of Excellence for Mathematics and Statistics of Complex Systems
2004 - 2008 ARC Network Complex Open Systems Network (COSNet)
2002 - 2006 ARC Discovery Advanced Computational and Analytic Studies in Lattice Statistical Mechanics and Applications
2005 The University of Melbourne MRGS Development and application of novel stochastic enumeration techniques
1999 - 2003 ARC Senior Research Fellowship Lattice Walks in Statistical Mechanics
2001 The University of Melbourne MRGS Computer Simulations of lattice polymers
Academic Board member
Associate Deans Learning and Teaching Forum
Bachelors of BioMed/BSc Standing Committee member
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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
Strategic Planning Committee