Research Interests
Research Groups
Extra Information
I am interested in solvable lattice models, an area of maths which offers exciting research possibilities in pure as well as applied mathematics. The study of solvable lattice models uses a variety of techniques, ranging from algebraic concepts such as Hecke algebras and quantum groups to analytic methods such as complex analysis and elliptic curves. Due to this wide variety of methods, the study of solvable lattice models often produces unexpected links between different areas of research. Currently I am studying such connections between enumerative combinatorics & statistical mechanics on the one hand, and symmetric polynomials, algebraic geometry & representation theory on the other.
Aside from the pure maths aspects of solvable lattice models, they provide useful frameworks for modeling real world phenomena. Examples of solvable lattice models that are widely used in applications are quantum spin chains and ladders as models for metals and superconductivity, random tilings as models for quasicrystals and exclusion processes as models for traffic and fluid flow.
Current Postgraduate Supervision
Name 
Thesis title 
Zeying CHEN 

John FOXCROFT 
"Combinatorial Enumeration and the Bethe Auzats." 
Past Postgraduate Supervision
Name 
Thesis title 
Caley FINN 
"The Asymmetric Exclusion Process with Open Boundaries" 
Alexander LEE 
"Loop models on random geometries" 
Anthony MAYS 
"Eigenvalue distributions in the complex plane" 
Anita PONSAING 
"Combinatorial aspects of the quantum Knizhnik  Zamolodchikov equation" 
Maria TSARENKO 
"Integrable Random Tiling Models" 
Current MSc Students
Name 
Project title 
Scott MASON 

Past MSc Students
Name 
Project title 
Kayed AL QASEMI 

Chunhua CHEN 
"SchrammLoewner Evolutions" 
John FOXCROFT 

Noon SILK 

Maria TSARENKO 
"Discretely Holomorphic Observables and Integrable Loop Models" 
Recent Grant History
Year(s) 
Source 
Type 
Title 
2014  2016 
ARC 
Discovery 
Multivariate polynomials:combinatorics and applications (080080) 
2009  2011 
ARC 
Discovery 
Polynomial representations of the Hecke algebra 
2008  2009 
ARC 
Linkage International 
Hecke algebras and hidden symmetries in quantum spin chains 
2007  2011 
ARC 
Discovery 
Statistical Topology and its Application to Deriving New Geometric Invariants 
2006  2008 
ARC 
Linkage International 
Exact dynamics of the asymmetric exclusion process with boundaries 
Responsibilities
Committees
 Research and Industry Committee
 Strategic Planning Committee