School of Mathematics and Statistics

  • Room: 192
  • Building: Peter Hall Building
  • Campus: Parkville

Research Interests

  • Exact solutions of lattice models
  • Statistical Mechanics
  • Enumerative combinatorics
  • Mathematical Physics
  • Integrable systems
  • Lattice polymer models

Research Groups


You can find all publications on their Find an Expert page

Find an Expert

Extra Information

I hold the position of Professor in Mathematics and Statistics of the University of Melbourne and am currently in the role of Deputy Dean of the Faculty of Science. Previously, I was Head of School/Department of Mathematics and Statistics between 2011-2016. I was also Director of the Melbourne Graduate School of Science/Associate Dean (Graduate Program) between 2009 and 2016. I currently hold an Australian Research Council Discovery Program grant on the Interplay of Topology and Geometry in Polymeric Critical Phenomena and am a Fellow of the Australian Mathematical Society. My area of expertise is mathematical statistical mechanics and, in particular, the area of phase transitions and critical phenomena of model polymer systems, namely lattice walk models, which lies within the discipline of mathematical physics. My 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. My Orcid ID Publications

Past Postgraduate Supervision

Name Thesis title
Debra 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"
Ruijie XU "Interacting Quarter-Plane Lattice Walk Problems: Solutions and Proofs"

Past Honours & 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 "A generalised model of a semi-flexible polymer at an adsorbing wall"

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


  • Academic Consultation Coordination Committees
  • AMSI Advisory Board
  • Bachelors of BioMed/BSc Standing Committee member
  • Buyers Committee (Business Services) member
  • Chancellor's Prize for PhD thesis in Tri-Faculty Group member
  • Deputy Dean
  • Employment Fundamentals Project Governance Committee
  • Engagement at Melbourne Academic Leadership Committee
  • Faculty of Science Education Executive (Chair)
  • Faculty of Science Indigenous Engagement Advisory Group (Chair)
  • Faculty of Science Planning and Resources Committee
  • Faculty Planning & Resources Committee member
  • Faculty Promotions and Appointments Committees (Chair)
  • MATRIX Board
  • MSE2025 Board
  • OEP Community and Advisory Board
  • University's Westpac Fellowship Committee Buyers Committee (Business Services)


  • Strategic Planning Committee