Professor JAN DE GIER
Position:
Head of School
Email:
Room:
113
Ext. Number:
49709
Webpage:
Research Groups:
Interests:
- Mathematical Physics
Recent Publications:
- Matrix product formula for Macdonald polynomials (2015) more
- The critical fugacity for surface adsorption of SAW on the honeycomb lattice is $1+sqrt{2}$ (2014) more
- Traffic disruption and recovery in road networks (2014) more
- Exclusion in a priority queue (2014) more
- A comparative study of Macroscopic Fundamental Diagrams of arterial road networks governed by adaptive traffic signal systems (2013) more
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.
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:
Zeying CHEN | |
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:
Chunhua CHEN | "Schramm-Loewner Evolutions" |
Maria TSARENKO | "Discretely Holomorphic Observables and Integrable Loop Models" |
Kayed AL QASEMI | |
John FOXCROFT | |
Noon SILK |
Recent Grant History:
Year(s) | Source | Type | Title |
---|---|---|---|
2014 - 2016 | ARC | Discovery | Multivariate polynomials:combinatorics and applications (080080) |
2007 - 2011 | ARC | Discovery | Statistical Topology and its Application to Deriving New Geometric Invariants |
2009 - 2011 | ARC | Discovery | Polynomial representations of the Hecke algebra |
2008 - 2009 | ARC | Linkage International | Hecke algebras and hidden symmetries in quantum spin chains |
2006 - 2008 | ARC | Linkage International | Exact dynamics of the asymmetric exclusion process with boundaries |
2005 | The University of Melbourne | MRGS | Combinatorial Structures of Exact Groundstates |
2003 - 2005 | ARC | Linkage International | Conformal invariance and stationary states |
Responsibilities:
MATRIX Director |
Committees:
Research and Industry Committee |
Strategic Planning Committee |