## 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) moreTraffic disruption and recovery in road networks (2014) moreA comparative study of Macroscopic Fundamental Diagrams of arterial road networks governed by adaptive traffic signal systems (2013) moreDiscrete holomorphicity and integrability in loop models with open boundaries (2013) moreARC Linkage Project Modeling large urban transport networks using stochastic cellular automata Interim Report V: The Effect of Bicycles on Bus Operations (2013) moreAll Selected PublicationsRSS Feed 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.

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

Anthony MAYS "Eigenvalue distributions in the complex plane"
Anita PONSAING "Combinatorial aspects of the quantum Knizhnik - Zamolodchikov equation"
Maria TSARENKO "Integrable Random Tiling Models"

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