Dr Richard BRAK
Senior Lecturer
School of Mathematics and Statistics
- Room: 197
- Building: Peter Hall Building
- Campus: Parkville Campus
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
- Complex Systems
- Discrete Mathematics & Algebraic Combinatorics
- Mathematical Physics & Statistical Mechanics
- Statistical Mechanics & Combinatorics
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.
Extra Information
My general interest lies in the mathematics of statistical mechanics and combinatorics.
Current Postgraduate Supervision
Name | Thesis title |
---|---|
John FOXCROFT | "Combinatorial Enumeration and the Bethe Auzats." |
William MOORE | "Bi-orthogonal Polynomials and the Combinatorics of Asymmetric Simple Exclusion Process" |
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" |
Will JAMES | "The enumeration of heaps and almost-convex polygons" |
Paul NIDRAS | "Critical behaviour of geometric cluster models" |
Judy-anne OSBORN | "Combinatorics of pavings and paths" |
Past 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 (080080) |
2003 - 2010 | ARC | Centre Of Excellence | ARC Centre of Excellence for Mathematics and Statistics of Complex Systems |
Responsibilities
- Chair of Web/IT Committee
- Department Database Co-ordinator
- Department WWW Coordinator
- IT Cluster Committee Dept Rep
- Lecture & 2nd Examiner Schedules
Committees
- IT/Web Committee
- Management Committee
- UGS Committee