Prof Jan DE GIER
Professor
School of Mathematics and Statistics
- Room: 194
- Building: Peter Hall Building
- Campus: Parkville
Research Interests
- Stochastic Processes
- Integrable models
- Mathematical Physics
- Combinatorics
Research Groups
Publications
You can find all publications on their Find an Expert page
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.
Past Postgraduate Supervision
Name | Thesis title |
---|---|
Zeying CHEN | "Exact solutions in multi-species exclusion processes" |
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" |
Current MSc Students
Name | Project title |
---|---|
William MEAD | "to be confirmed" |
Past Honours & MSc Students
Name | Project title |
---|---|
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
Year(s) | Source | Type | Title |
---|---|---|---|
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 |
Responsibilities
- AMSI representative
- MATRIX Director
Committees
- Belz Committee
- Strategic Planning Committee