- Stochastic Processes
- Integrable models
- Mathematical Physics
X. Zhang, Fakai Wen, J. de Gier. T-Q relations for the integrable two-species asymmetric simple exclusion process with open boundaries. Journal of Statistical Mechanics: Theory and Experiment, 2019, 014001 (28pp), 2019. doi: 10.1088/1742-5468/aaeb4a.
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.
Z. Chen, J. de Gier, I Hiki, T. Sasamoto. Exact Confirmation of 1D Nonlinear Fluctuating Hydrodynamics for a Two-Species Exclusion Process. Physical Review Letters, 120, 240601, 2018. doi: 10.1103/PhysRevLett.120.240601.
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.
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.
Past Postgraduate Supervision
|Caley FINN||"The Asymmetric Exclusion Process with Open Boundaries"|
|John FOXCROFT||"Combinatorial Enumeration and the Bethe Ansatz"|
|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"|
|Alessandra VITTORINI ORGEAS||"Yang-Baxter Integrable Dimers and Fused Restricted-Solid-On-Solid Lattics Models"|
Past Honours & MSc Students
|Kayed AL QASEMI||"The Inhomogeneous Asymmetric Simple Exclusion Process"|
|Chunhua CHEN||"Schramm-Loewner Evolutions"|
|John FOXCROFT||"A Comparative Study of Traffic Models"|
|Scott MASON||"Quantum Random Walks"|
|Noon SILK||"Minimal resource topological quantum computation"|
|Maria TSARENKO||"Discretely Holomorphic Observables and Integrable Loop Models"|
Recent Grant History
|2019 - 2021||ARC||Discovery||Matrix product multi-variable polynomials from quantum algebras|
|2014 - 2016||ARC||Discovery||Multivariate polynomials:combinatorics and applications|
|2014 - 2016||ARC||Centre Of Excellence||ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS)|
|2012 - 2014||ARC||Linkage||Modelling large urban transport networks using stochastic cellular automata|
|2009 - 2011||ARC||Discovery||Polynomial representations of the Hecke algebra|
|2007 - 2011||ARC||Discovery||Statistical Topology and its Application to Deriving New Geometric Invariants|
- Academic Board member
- AMSI representative
- Chair of Management Committee
- Head of School
- MATRIX Director
- School Seminar Coordinator
- Belz Committee
- Executive Committee
- Management Committee
- Postgraduate Programs Committee
- Strategic Planning Committee