- Mathematical Physics
- Algebra, Number Theory & Representations
- Discrete Mathematics & Algebraic Combinatorics
- Mathematical Physics & Statistical Mechanics
L. Zhang, C. Finn, T. Garoni, J. de Gier. Behaviour of traffic on a link with traffic light boundaries. Physica A: Statistical Mechanics and its Applications, 503, 116-138, 2018. doi: 10.1016/j.physa.2018.02.201.
A. Garbali, J. de Gier, M. Wheeler. A New Generalisation of Macdonald Polynomials. Communications in Mathematical Physics, 352, 773-804, 2017. doi: 10.1007/s00220-016-2818-1.
J. de Gier, Gyorgy Z Feher, Bernard Nienhuis, Magdalena Rusaczonek. Integrable supersymmetric chain without particle conservation. Journal of Statistical Mechanics: Theory and Experiment, 2016, 023104 (28pp), 2016. doi: 10.1088/1742-5468/2016/02/023104.
J. de Gier, M. Wheeler. A Summation Formula for Macdonald Polynomials. Letters in Mathematical Physics, 106, 381-394, 2016. doi: 10.1007/s11005-016-0820-3.
Luigi Cantini, A. Garbali, J. de Gier, M. Wheeler. Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries. Journal of Physics A: Mathematical and Theoretical, 49, 444002 (23pp), 2016. doi: 10.1088/1751-8113/49/44/444002.
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
|John FOXCROFT||"Combinatorial Enumeration and the Bethe Auzats."|
Past Postgraduate Supervision
|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
Past MSc Students
|Kayed AL QASEMI|
|Chunhua CHEN||"Schramm-Loewner Evolutions"|
|Maria TSARENKO||"Discretely Holomorphic Observables and Integrable Loop Models"|
Recent Grant History
|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|
- AMSI representative
- Chair of Management Committee
- Head of School
- MATRIX Director
- School Seminar Coordinator
- Belz Committee
- Executive Committee
- Management Committee
- Postgraduate Programs Committee
- Research and Industry Committee
- Strategic Planning Committee