Dr Richard BRAK

Senior Lecturer

School of Mathematics and Statistics

  • Room: 197
  • Building: Peter Hall Building
  • Campus: Parkville

Research Interests

  • Enumerative combinatorics
  • Statistical Mechanics
  • Stochastic Processes
  • Critical Phenomena (phase transitions)
  • Markov processes
  • Combinatorics
  • Orthogonal functions and polynomials
  • Polymers
  • Modelling of biological systems

Research Groups

Recent Publications

  • R. Brak, W. Moore. Bi-orthogonal polynomial sequences and the asymmetric simple exclusion process. Journal of Physics A: Mathematical and Theoretical, 48, 315205 (15pp), 2015. doi: 10.1088/1751-8113/48/31/315205.

  • R. Brak, W. Galleas. Constant term solution for an arbitrary number of osculating lattice paths. Letters in Mathematical Physics, 103, 1261-1272, 2013. doi: 10.1007/s11005-013-0646-1.

  • R. Brak, J Essam. Simple Asymmetric Exclusion Model and Lattice Paths: Bijections and Involutions. Journal of Physics A - Mathematical and Theoretical, 45, 494007 (22pp), 2012. doi: 10.1088/1751-8113/45/49/494007.

  • R. Brak, G. Iliev, T. Prellberg. An Infinite Family of Adsorption Models and Restricted Lukasiewicz Paths. Journal of Statistical Physics, 145, 669-685, 2011. doi: 10.1007/s10955-011-0306-8.

  • R. Brak, G. Iliev, A. Owczarek, S. Whittington. The exact solution of a three-dimensional lattice polymer confined in a slab with sticky walls. J. Phys. A: Math. Theor., 43, 135001 (12pp), 2010. doi: 10.1088/1751-8113/43/13/135001. PDF.

View all

Extra Information

My general interest lies in the mathematics of statistical mechanics and combinatorics.

Past Postgraduate Supervision

Name Thesis title
Nicholas BEATON "Combinatorics of Lattice Paths and Polygons"
Paul FIJN "The combinatorics and graph theory of stochastic interface and lattice path problems"
Caley FINN "The Asymmetric Exclusion Process with Open Boundaries"
John FOXCROFT "Combinatorial Enumeration and the Bethe Ansatz"
Will JAMES "The enumeration of heaps and almost-convex polygons"
William MOORE "Biorthogonal polynomial sequences and the asymmetric simple exclusion process"
Paul NIDRAS "Critical behaviour of geometric cluster models"
Judy-anne OSBORN "Combinatorics of pavings and paths"

Current MSc Students

Name Project title

Past Honours & MSc Students

Name Project title
William MOORE
Andrew OPPENHEIM "Directed walkers on the square and triangular planar lattices"
William TOM
Tianyu (Tim) YANG

Recent Grant History

Year(s) Source Type Title
2014 - 2016 ARC Discovery Multivariate polynomials:combinatorics and applications


  • Lecture Schedules


  • Engagement and Publicity Committee
  • IT/Web Committee
  • UGS Committee