Professor Jan de Gier
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 stochastic processes, 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 stochastic processes, 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.
Research Interests:
Enumerative combinatorics
Hecke algebras
Quantum Groups
Solvable lattice models
Statistical mechanics
Stochastic Processes
Symmetric polynomials
Projects
Publications
Books
(2019). 2017 MATRIX Annals.
(Wood, D., De Gier J., Praeger C. E., & Tao T., Ed.).MATRIX Book Series. 2, doi: 10.1007/978-3-030-04161-8
(2018). 2016 MATRIX Annals.
(De Gier, J., Praeger C. E., Wood D. R., & Tao T., Ed.).MATRIX Book Series. 1, 656. doi: 10.1007/978-3-319-72299-3
Book Chapters
(2019). A Curious Mapping Between Supersymmetric Quantum Chains.
(D., W., De Gier J., Praeger C. E., & Tao T.., Ed.).2017 MATRIX Annals. 2017 MATRIX Annals, 167 - 184. doi: 10.1007/978-3-030-04161-8_12
(2019). A Metropolis-Hastings-Within-Gibbs Sampler for Nonlinear Hierarchical-Bayesian Inverse Problems.
(Wood, D. R., De Gier J., Praeger C. E., & Tao T., Ed.).2017 MATRIX Annals. 3 - 12. doi: 10.1007/978-3-030-04161-8_1
(2019). Optimization Methods for Inverse Problems.
(Wood, D., Ed.).2017 MATRIX Annals. doi: 10.1007/978-3-030-04161-8_9
(2019). Wider contours and adaptive contours.
(Wood, D., De Gier J., Praeger C. E., & Tao T., Ed.).2017 MATRIX Annals. 2, 79-98. doi: 10.1007/978-3-030-04161-8_7
Invited talks, refereed proceedings and other conference outputs
(2019). Dynamical Universality Class of the Nagel–Schreckenberg and Related Models.
Traffic and Granular Flow '17. 53 - 60. doi: 10.1007/978-3-030-11440-4_7
(2019). Limit shape of the asymmetric five vertex model.
ANZAMP Annual Meeting 2019.
(2019). Current distribution function for the Arndt-Heinzel-Rittenberg model.
Curiosity-Driven Physics: From Algebras to Quantum Chains and Statistical Mechanics.
(2018). GUE distribution in a two-species exclusion processes.
Integrable Systems 2018.
(2018). Six vertex limit shape outside the free fermion point.
Gaussian Free Fields and Related Topics.
(2018). A mathematician’s survival guide.
AustMS Early Career Workshop.
(2018). Non-Gaussian current distribution functions in multi-component particle systems.
ACEMS Workshop on Multiscale Models 2018.
(2016). Applications of the Bethe ansatz for the ASEP with open boundaries.
Infinite Analysis 16, New Developments in Integrable Systems.
(2016). A lattice supersymmetric model violating fermion number conservation .
New Trends in Low Dimensional Physics: Quantum Integrability and Applications.
(2016). Multi-species ASEP and Macdonald/Koornwinder polynomials.
Driven Stochastic Transport in Low-Dimensional Systems.
(2016). Matrix product for Macdonald polynomials and generalisations.
Integrable Systems 2016.
(2016). Matrix product and sum rule for Macdonald polynomials.
28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC).
(2016). Applications of the Bethe ansatz for the finite ASEP with open boundaries.
New approaches to non-equilibrium and random systems: KPZ integrability, universality, applications and experiments.
(2016). Multi-species exclusion process and Macdonald polynomials.
Infinite Analysis 16, New Developments in Integrable Systems.
Journal Articles
(2019). Kardar-Parisi-Zhang universality of the Nagel-Schreckenberg model.
Physical Review E. 100(5), 052111. doi: 10.1103/PhysRevE.100.052111
(2019). T-Q relations for the integrable two-species asymmetric simple exclusion process with open boundaries.
Journal of Statistical Mechanics: Theory and Experiment. 2019(1), 014001. doi: 10.1088/1742-5468/aaeb4a
(2018). Exact Confirmation of 1D Nonlinear Fluctuating Hydrodynamics for a Two-Species Exclusion Process.
Physical Review Letters. 120(24), 240601. doi: 10.1103/PhysRevLett.120.240601
(2018). Behaviour of traffic on a link with traffic light boundaries.
Physica A: Statistical Mechanics and its Applications. 503, 116 - 138. doi: 10.1016/j.physa.2018.02.201
(2017). A New Generalisation of Macdonald Polynomials.
Communications in Mathematical Physics. 352(2), 773 - 804. doi: 10.1007/s00220-016-2818-1
(2016). Finite-size corrections for universal boundary entropy in bond percolation.
SciPost Physics. 1(2), 012. doi: 10.21468/SciPostPhys.1.2.012
(2016). Integrable supersymmetric chain without particle conservation.
Journal of Statistical Mechanics: Theory and Experiment. 2016(2), 23104. doi: 10.1088/1742-5468/2016/02/023104
(2016). A summation formula for Macdonald polynomials.
Letters in Mathematical Physics. 106(3), 381-394. doi: 10.1007/s11005-016-0820-3
(2016). Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries.
Journal of Physics A: Mathematical and Theoretical. 49(44), 444002-444002. doi: 10.1088/1751-8113/49/44/444002
(2015). Matrix product formula for Macdonald polynomials.
Journal of Physics A: Mathematical and Theoretical. 48(38), 384001. doi: 10.1088/1751-8113/48/38/384001
(2014). Exclusion in a priority queue.
Journal of Statistical Mechanics: Theory and Experiment. 2014(7), P07014. doi: 10.1088/1742-5468/2014/07/P07014
Technical reports and unrefereed outputs
(2016). A new generalisation of Macdonald polynomials, arXiv preprint.
(2016). Study of Traffic Speed Limits.
