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Dr Jan DE GIER
	Position:	ARC Queen Elizabeth II Fellow
	Email:	J.Degier@ms.unimelb.edu.au
	Room:	205
	Ext. Number:	46603
	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: Selected Publications \| Publications RSS Feed Punctured plane partitions and the q-deformed Knizhnik--Zamolodchikov and Hirota equations(2008) more Maths Matters: Back to the future(2008) more Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries(2008) more The Razumov-Stroganov conjecture: Stochastic processes, loops and combinatorics(2007) more Editorial of Australian Mathematical Society Gazette Volume 33 Issue 5(2006) more
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:

Anita PONSAING	"Combinatorial aspects of the quantum Knizhnik - Zamolodchikov equation"
Anthony MAYS	"Eigenvalue distributions in the complex plane"
Nicholas BEATON	"Exact Solutions of Polygons and Random Walks."

Current Honours Students:

Recent Honours Students:

"Schramm-Lowner Evolutions"

Subject(s) Currently Teaching:

Integrable Models (Semester 2, 2009)

Recent Grant History:

Year(s)	Source	Type	Title
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 Shepherd

Committees:

Recruitment and Publicity Committee

RGS Committee (Discovery Shepherd)

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