01
Overview
Mathematics at UQ, which during 2003
–
8 was part of the
School of Physical Sciences
, covers all five
4

digit codes, though no significant quantity of data in 0199 has been submitted. Mathematics in the
School has a strong interdisciplinary
tradition, with a significant number of staff on joint
appointments (Goodhill, Queensland Brain Institute 50

50%; McLachlan, Institute for Molecular
Bioscience 80

20%; Possingham, School of Biological Sciences 50

50%; Richardson, CSRIO Marine
Research 50

5
0%).
Due to the interdisciplinary nature of the Applied Mathematics group in the School, the research
output of a number of high

profile researchers, such as Richardson and Possingham (Federation
Fellow), is not reflected in the 01 data. Their publications
contain an even mix of mathematics and
other discipline
contents, and under the ERA guidelines could not be claimed as 80
–
100%
Mathematics.
Pure Mathematics:
Key areas of strength are Discrete Mathematics and Analysis. The former
is concentrated in the
C
entre for Discrete Mathematics and Computing
, with emphasis on
combinatorial group theory, design theory, graph theory and interdisciplinary applications,
particularly in bioinformatics and sequence analysis. Research in analysis focused on
ordinary and pa
rtial differential equations, both theoretical and analytic aspects, with a
more recent emphasis on geometric evolution equations. The appointment of Warnaar to
the Chair of Pure Mathematics in 2008 added an international profile in algebra and number
theo
ry, further strengthened by subsequent junior appointments.
Papers submitted for peer review provide a representative sample of the various areas of research
activity.
Applied Mathematics:
Applied Mathematics at UQ includes topics of high
national/interna
tional significance. This includes the modelling of endangered species and
threatened ecosystems, marine modelling and sustainable fisheries, urban populations and
population networks, effectiveness of drugs, modelling of brain function and risk modelling.
Modelling in the physical and engineering sciences includes optimization, continuum
mechanics and diffusion processes in heterogeneous environments and dynamical systems.
Numerical and Computational Mathematics:
This has been an area of major strength a
t UQ,
both in the development and analysis of new techniques for solving stochastic differential
equations and in the application to important problems in the chemical and biological
sciences. The
Advanced Computational Modelling Centre
has focused on a ra
nge of
problems including simulation of stochastic chemical and biological kinetics, genetic
simulation and population dynamics. The centre pioneered new and effective techniques for
accurately solving stochastic differential equations.
Statistics:
Expert
ise in the group spans many areas of Statistics and Probability, both
theoretical and applied.
The development and use of modern computational methods in
statistical modelling is a common thread through much of the research.
Critical expertise
includes t
he areas of applied probability, computational statistics, design of experiments,
finite mixture modelling, machine learning, multivariate analysis and stochastic processes.
Mathematical Physics:
Research is concentrated in the
Centre for Mathematical Phy
sics
, with
a focus on exactly solvable models arising in condensed matter physics, such as Bose
–
Einstein condensates, lattice spin systems and superconductors.
Fundamental
understanding of these systems is important in advancing the development of quantum
technologies. Members of the Centre have played a key role in unravelling the mathematical
structures underpinning solvability, such as quantum groups, Hopf algebras and infinite

dimensional Lie algebras.
Publication Profile
The traditional outlets for
mathematics research are peer

reviewed journal articles, with >92% of
research output covered by the ranked journal

list. A majority of journal publications are in A* /A
ranked journals (eg. 65% A*/A in Statistics (0104) and 84% A*/A in Mathematical Physic
s (0105).
In 2003
–
8 a number of influential research monographs were published:
RY Rubinstein,
DP Kroese:
Simulation and the Monte Carlo Method
, 2nd Edition,
2007. Considered a classic monograph in the theory and applications of simulations;
around 2500 ci
tations on Google Scholar.
GJ McLachlan
,T Krishnan:
The EM algorithm and extensions
, 2nd Edition, 2008.
Authoritative text on the expectation

maximization algorithm, a broadly applicable
method to compute maximum likelihood estimates in statistical model
ling; around
3000 citations on Google Scholar.
Other noteworthy monographs include RY Rubinstein,
DP Kroese:
The Cross

Entropy Method:
A
Unified Approach to Combinatorial Optimization, Monte

Carlo Simulation, and Machine Learning
,
(2004) and
GJ McLachla
n
, K

A Do,
C Ambroise:
Analyzing Microarray Gene Expression Data
, (2004).
Capacity and Environment
The apportioned RHD headcount in Mathematics (at the respective 4

digit levels) are, 25.3, 14.6, 2.9,
28.4, 14 (Total 85.2). 2003
–
8 saw a total of 56 PhD a
nd 3 MPhil completions.
Mathematics was part of 3 successful bids for ARC Centres:
COE for Mathematics and Statistics of Complex Systems;
received funding of
>$10.9M for 2003
–
7 plus $1.8M for 2008
–
10. UQ node CI is P Pollett.
Centre for Complex Systems
; received funding of >$7.1M for 2003
–
8. CIs of the
Centre from Mathematics were Adams, Burrage, McLachlan and Pailthorpe.
Centre for Bioinformatics
; received funding of $3.6M for 2003
–
7. The Centre became
an ARC COE in 2008 and received an additional $ 3.
3M for 2008
–
10. The principle
node of the Centre is at UQ, with 3 mathematicians (Burrage, McLachlan and
Pailthorpe) among the CIs.
In 2008, in a major strategic initiative in Resource Management, the University reached a joint
agreement with the Queensland Department of Primary Industries and Fisheries (DPI&F) to create
the UQ
Centre for Application in Natural Resource Mathematics
(CA
RM). The Centre has secured
initial funding for 5 years, and is supported by $500K from DPI&F and $2.41M from UQ. CARM
employs mathematicians and statisticians with expertise in fisheries, marine ecosystems and
population modelling.
A number of UQ mathemat
icians have been the recipients of major prizes and distinctions:
Bryant, 2007 Hall Medal of The Institute of Combinatorics and its Applications
Burrage, ARC Federation Fellow 2003
–
8
McLachlan, ISI Highly Cited Author
Possingham, Elected Fellow of the Aust
ralian Academy of Science, 2005; ARC
Federation Fellow 2007
–
11
Warnaar, Elected Fellow of the Australian Academy of Science, 2008
5 year Fellowships, and year of award:
Bryant, QEII Fellowship 2002 and 2007
McLachlan, ARC Professorial Fellowship, 2007
Kroe
se, ARC Professorial Fellowship, 2009
Staff held Principal Editorial Roles in a number of A*/ A Journals:
Journal of Combinatorial Theory A;
Journal of Combinatorial Designs; Biometrics; Statistics and Computing
;
Computational Statistics and
Data Analysis
.
Collaboration
Mathematics at UQ fosters strong multidisciplinary links across a wide range of disciplines.
A
notable example is UQ's centre for
Applied Environmental Decision Analysis (
AEDA) led by
Possingham.
AEDA includes quantitative ecologists with
backgrounds in mathematics, geography
and biology, and uses statistical and applied mathematics tools for modelling ecological systems,
analysing complex ecological data and providing tools to solve environmental decision

making
problems.
Its Eureka Priz
e winning conservation software is currently in use in more than 100
countries.
During 2003
–
8, Mathematics housed the inter

disciplinary
Advanced Computational Modelling
Centre
led by Burrage.
The focus of the centre was the development of computational m
ethods and
tools for solving problems in Biology, Medicine and Engineering. The topology optimization group in
Mathematics has had an ongoing collaboration with material scientists at UWA on the design of
shape

optimized bone implant scaffolds.
Several ARC
Linkage Grants were awarded to mathematicians in the School, including:
Prof. P Pollett,
Animal movement between populations deduced from family trees:
a
test case on dugongs in southern Queensland
, $225K; 2008
–
10 with Dr. J Lanyon,
School of Integrative Biology, J Ovenden and D. Broderick, QDPI&F. Partner
organisations are QDPI&F, Consolidated Rutile Ltd and Sea World
Dr N Bordes,
The Queensland Historical Atlas
, $602K; 2007
–
09 with UQ
CIs from 4
Schools across three different faculties, and external CIs from the Partner
Organisation, the
Queensland Museum
Prof H Possingham and Dr A Richardson,
Resilience of Moreton Bay to climate change: Links
between nutrient inputs and plankton dynamics
, $720K;
2008
–
11 with external CIs from the
Australian Rivers Institute, Griffith University. Partner organisations are Healthy Waterways
Partnership and Environmental Protection Agency, now Department of Environment and
Resource Management (DERM).
Other
Eccleston
served on the Queensland Government Transport Statistical Advisory Board 2001
–
6.
Gould serves on the C18 Commission
–
Mathematical Physics, of the IUPAP.
McLachlan is Member of the ARC College of Experts 2008
–
10.
Patent: P Adams, D Bryant, S Long, M Smythe
and TT Tran, Common protein surface shapes,
PCT/AU03/00137 2003.
In 2007 members of the Centre for Mathematical Physics, chaired by Gould, played a lead
role in the successful bid to host the highly prestigious
XXIVth International Conference on
Statistic
al Physics
. STATPHYS24 was held in Queensland in July 2010. Keynote speakers
included 2 Nobel Laureates and a Fields Medallist.
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