Associate Professor Jan DE GIER

Position: Associate Professor/Reader
Email: J.Degier@ms.unimelb.edu.au
Room: 164
Ext. Number: 49709
Webpage: www.ms.unimelb.edu.au/~degier/
Research Group:- Algebra, Number Theory & Representations
- Discrete Mathematics & Algebraic Combinatorics
- Mathematical Physics & Statistical Mechanics
Interests: - Mathematical physics

Recent Publications:

  • 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
  • A comparative study of Macroscopic Fundamental Diagrams of arterial road networks governed by adaptive traffic signal systems (2013) more
  • Discrete holomorphicity and integrability in loop models with open boundaries (2013) more
  • Deformed Kazhdan-Lusztig elements and Macdonald polynomials (2012) more

All Selected Publications

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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:

Caley FINN "The Asymmetric Exclusion Process with Open Boundaries"
Daniel SCHEPISI

Past Postgraduate Supervision:

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:

Noon SILK

Past MSc Students:

Chunhua CHEN "Schramm-Loewner Evolutions"
Maria TSARENKO "Discretely Holomorphic Observables and Integrable Loop Models"
Kayed AL QASEMI
John FOXCROFT

Subject(s) Currently Teaching:

MAST30021 (620-324) Complex Analysis (Semester 2, 2014)

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:

ARC Discovery Coordinator
Postgraduate Coursework Coordinator

Committees:

Masters Committee (Postgraduate Coursework Coordinator)
RGS Committee (Discovery Coordinator)