Institution: The Australian National University
Dr Murray Batchelor
|
2002 |
2003 |
2004 |
| Funding |
$57,000 |
$58,000 |
$60,000 |
Title: Solvable models and pattern formation: quantum
spin ladders, combinatorics and stromatolite morphogenesis
Summary:
The aim of this project is to develop new applications of exactly
solved models in statistical mechanics. These include the study of
quantum spin ladders of great interest in condensed matter
physics. The physical properties of new and existing models will be
derived to provide valuable benchmarks and predictions for future
theoretical and experimental work. We will also undertake the study
and development of a set of remarkable conjectures relating the
properties of a solvable model to an established area of
combinatorics. Another aspect of this project involves the
investigation of the origins, growth and form of ancient
stromatolites.
Institution: Australian National University -
Institute of Advanced Studies
Prof V V Bazhanov and Prof RJ Baxter
|
2002 |
2003 |
2004 |
| Funding |
$105,000 |
$106,000 |
$107,000 |
Title: Solvable models on regular and random lattices
in statistical mechanics and field theory
Summary:
There are only a few solvable models in statistical mechanics and
field theory, but those that are known give deep insights into the
cooperative behaviour that characterizes a critical point, as well as
leading to fascinating mathematics. The two chief investigators have
been at the forefront of this field for many years. Currently there
are many notable exciting challenges they wish to address: the
relationship between Tutte's work on dichromatic polynomials and
matrix models, the outstanding problem of calculating the order
parameters of the chiral Potts model, and the eigenvalue spectra of
the transfer matrices that occur in integrable models.
Institution: Monash University
Prof. Alan Bishop
Prof. RF Gunstone
Dr B Clarke
Dr DJ Corrigan
|
2002 |
2003 |
2004 |
| Funding |
$25,000 |
$33,000 |
$33,000 |
Title: Values in mathematics and science education:
mapping the relationships between pedagogical practices and student
outcomes
Summary:
Mathematics and science in institutes both involve the teaching of
values. Some value outcomes are intended by the teachers and are
explicitly taught, particularly in science, while other values are
only implicitly present in classroom practices, as is typically the
case with mathematics. What is not yet known is what values students
learn from different teachers and from their practices, and how these
learned values impact on student engagement with these subjects. This
project will explore the relationships between the values embedded in
the pedagogical practices of primary and secondary teachers of
mathematics and science, and student values outcomes.
Institution: The University of Adelaide
Dr Pier Bouwknegt and Dr M Varghese
|
2002 |
2003 |
2004 |
| Funding |
$60,000 |
$90,000 |
$90,000 |
Title: Twisted K-theory and its application to String Theory and Conformal Field Theory
Summary:
String Theory is, at present, the only consistent theory of quantum
gravity. Recently, twisted K-theory was proposed as the algebraic
structure underlying the classification of D-branes, i.e. solitonic
extended objects, in certain closed string backgrounds. In this
project we aim to advance our understanding of the properties of
twisted K-theory in the context of String Theory and Conformal Field
Theory. The ultimate goal is to find the appropriate K-theory
classifying D-branes in arbitrary closed string backgrounds or,
similarly, classifying boundary Conformal Field Theories. It has
already emerged that the K-theory of
C*-algebras will play an
important role.
Institution: The University of Adelaide
Prof. Michael Brooks
|
2002 |
2003 |
2004 |
| Funding |
$78,712 |
$64,512 |
$64,512 |
Title: A framework for the generation of
high-precision and quantifiable methods in computer vision.
Summary:
Computer vision is concerned with many challenging problems assuming a
variety of mathematical forms. An example might be computing new views
of a 3D scene given some existing views. This project aims to develop
a procedural framework that enables a wide class of problems to be
solved with both high precision and a quantifiable level of
accuracy. Many practical vision-based applications will stand to gain
from this work.
Institution: The University of Melbourne
Prof Timothy Brown and Dr A Xia
Title: Stein's method for probability approximation
Summary:
Data of counts in time, such as incoming calls in telecommunications
and the clusters of palindromes in a family of herpes-virus genomes,
arise in an extraordinarily diverse range of fields from science to
business. These problems can be modelled by sums of random variables
taking values 0 and 1 in probability theory, thus permitting
approximate calculations which are often good enough in practice. This
project will obtain such approximate solutions and estimate the errors
involved. Applications include analysis of data in insurance, finance,
flood prediction in hydrology.
Institution: The University of Queensland
Dr Darryn Bryant, Dr P Adams and Dr K Mitchelson
|
2002 |
2003 |
2004 |
2005 |
2006 |
| Funding |
$91,839 |
$93,411 |
$93,411 |
$93,411 |
$93,411 |
Title: Mutagenesis and combinatorial algorithms for
sequencing problematic genomic regions.
Summary:
This project will develop a remarkable and original approach to DNA
sequencing with potential to radically improve the speed, accuracy and
effectiveness of existing sequencing technologies. It is especially
useful for dealing with difficult-to-sequence genomic regions and has
implications for all sequencing projects, including completion of the
Human Genome Project. The approach involves generating, and wholly or
partially sequencing, mutated copies of problematic regions of the
target genome. Advanced combinatorial algorithms are then used to form
highly probable alignments between strings and determine the unknown
sequence. The approach has additional benefits in detecting
single-nucleotide polymorphisms and sequencing errors.
Institution: The University of Adelaide
Prof. Alan Carey
|
2002 |
2003 |
2004 |
| Funding |
$35,000 |
$35,000 |
$35,000 |
Title: Novel geometric invariants
Summary:
Quantum theory is the language of fundamental physics, it describes
the small scale structure of matter and possibly
space-time. Sophisticated models in condensed matter physics and
string theory have exposed geometric and topological structure as
basic building blocks of the theory. Issues thrown up by quantum
theory are very similar to, and have provided techniques to solve,
problems in the geometry of three and four dimensional
manifolds. Exciting two way exchanges of methods, problems and
solutions have emerged. This project aims to settle fundamental
questions in the interaction between these two fields.
Institution: The University of New South Wales
Dr Ruth Corran
|
2002 |
2003 |
2004 |
2005 |
| Funding |
$45,888 |
$47,226 |
$47,226 |
$47,226 |
Title: Braid monoids, presentations and normal forms.
Summary:
Braid groups arise naturally in various areas of mathematics, physics
and computer science including knot theory, Lie theory, quantum groups
and cryptography. There is a uniform geometric description of braid
groups; however this is not the case algebraically. This project aims
to find the connections between the algebra, combinatorics and
geometry of braid groups in order to obtain a uniform algebraic
description. This generalisation will allow advances in the related
areas of mathematics and physics. In addition to theoretical results,
new algorithms for calculating in braid groups will be given, which
can then be implemented computationally.
Institution: The University of New South Wales
Prof. Michael Cowling
|
2002 |
2003 |
2004 |
2005 |
2006 |
| Funding |
$78,792 |
$82,000 |
$86,500 |
$70,000 |
$70,000 |
Title: Iwasawa N-Groups
Summary:
Semisimple Lie groups and related objects are important in
mathematics, theoretical physics (e.g., quantum mechanics and string
theory), theoretical computer science (e.g., construction of
expanders), and many other areas. They may be studied from different
points of view - algebraic, analytic, geometric and
representation-theoretic - and these different studies find different
applications. The project aims to synthesize the different points of
view, to understand their fundamental unity, and to allow results of
one type to be translated into another context.
Institution: The University of Sydney
Prof Norman Dancer
|
2002 |
2003 |
2004 |
| Funding |
$70,045 |
$80,000 |
$80,000 |
Title: Abstract methods for nonlinear partial
differential equations
Summary:
To use abstract methods to study nonlinear partial differential
equations where nonlinear effects dominate and where the diffusion is
possibly small. These equations arise in many applications of
mathematics such as population models and catalysis theory.
Institution: Australian National University -
Institute of Advanced Studies
Dr Jennifer Davoren and Dr T Moor
|
2002 |
2003 |
2004 |
| Funding |
$61,184 |
$90,000 |
$92,000 |
Title: Mathematical, logical and computational
foundations of hybrid control systems, and their application to design
and synthesis problems in control engineering
Summary:
Hybrid control systems are mathematical models of heterogeneous
systems consisting of digital computer components interacting in
real-time with continuous physical processes. Their many engineering
applications include air traffic control, medical technology and
automated transport. Motivated by such safety-critical and
high-confidence applications, the project aims to develop a unified
framework of mathematical logics adequate to formally represent and
reason about the structure, behaviour, and properties of hybrid
control systems, and use this to develop methodologies for
automatically synthesising hybrid control programs that are provably
correct with respect to their specifications. Other outcomes include
prototype software implementations of hybrid controller design tools.
Institution: Queensland University of Technology
Dr Carmel Diezmann
|
2002 |
2003 |
2004 |
2005 |
| Funding |
$50,000 |
$52,000 |
$52,000 |
$52,000 |
Title: A Longitudinal Study of the Development of
Primary Students' Knowledge About the Properties of Spatially-Oriented
Diagrams in Mathematics
Summary:
Diagrams are important tools for the solution of novel (non-routine)
problems and the organization of data because they integrate
information in ways that facilitate reasoning. Diagrams also underpin
many technological applications (E.g., hyperlinks on web-pages from a
"network"). Ground-breaking research in the US with adults has
identified the properties of general-purpose diagrams (networks,
matrices, hierarchies). These properties constitute the "building
blocks" of diagrammatic knowledge - like grammar in language. This
study investigates children's knowledge of the properties of diagrams
and the formation of this fundamental knowledge. The outcomes will
enhance 21st century mathematical literacy, guide curriculum
development, and inform teacher education.
Institution: The University of New South Wales
Prof. Anthony Dooley and Dr G Mortiss
|
2002 |
2003 |
2004 |
2005 |
2006 |
| Funding |
$95,000 |
$125,000 |
$125,000 |
$60,000 |
$60,000 |
Title: Group orbits in harmonic analysis and ergodic theory.
Summary:
Researchers from many areas need a type of mathematical analysis which
involves the behaviour of a system - which may be a set of data points
- under repeated application of some operation or group of
operations. The structures arising from this kind of process are known
as group orbits. The project gives information about their nature. Two
major types of orbits are considered, coming from actions of discrete
groups on measure spaces, and from smooth actions of Lie groups on
manifolds, where powerful geometric methods are available. The project
will yield new understandings of entropy, and new approaches to
Fourier analysis.
Institution: The University of Newcastle
Dr Vladimir Estivill-Castro, Dr MR Fellows and Dr
ME Houle
|
2002 |
2003 |
2004 |
2005 |
| Funding |
$47,200 |
$52,529 |
$54,252 |
$27,557 |
Title: Approximate proximity for applications in data
mining and visualization
Summary:
Data Mining, pattern recognition and visualization of relational
information are all important data analysis techniques in which it is
essential to determine which data points are in the vicinity of
others. The huge size of the data sets involved and the need for
real-time interaction preclude the use of conventional methods for the
precise computation of the proximity information required. This
project will develop efficient algorithms and data structures for
gathering high-quality approximations of the full proximity
information, and will use these innovations as the basis for new,
practical tools for visualization, and clustering in data mining.
Institution: The University of Melbourne
Dr Anandaswarup Gadde, and Prof. CF Miller
|
2002 |
2003 |
2004 |
| Funding |
$25,000 |
$30,000 |
$32,000 |
Title: Geometric Group Theory
Summary:
Groups arise naturally as symmetries of geometric objects. Often
groups have an interesting geometric structure obtained by thinking of
these geometric objects coursely. This project aims to study the
subgroup structure of such groups and obtain homological, geometric
and algorithmic information. It further investigates natural
decompositions of groups with geometric structure along special
subgroups so that the factors have simpler properties.
Institution: The University of Western Australia
Dr Jiti Gao, Prof. Dr ML King and Prof. Dr D Tjostheim
|
2002 |
2003 |
2004 |
| Funding |
$27,000 |
$37,000 |
$35,000 |
Title: Nonparametric and Semiparametric Approaches in
Nonlinear Time Series Econometrics and Financial Econometrics
Summary:
This research proposal involves new theoretical investigations using
nonparametric and semiparametric approaches in high dimensional
nonlinear economic and financial dynamical systems.
The main aims of this proposal are
- to make new theoretical investigations of high dimensional
nonlinear economic and financial dynamical models which incorporate
to varying degrees, nonlinearity, and additivity;
- to develop novel computational procedures and programmes for the
necessary statistical inference associated with new high dimensional
nonlinear dynamical models; and
- to apply the techniques and programmes to improve economic and
financial model building and forecasts from better models.
Institution: The University of Queensland
Dr Merrilyn Goos
|
2002 |
2003 |
2004 |
| Funding |
$20,000 |
$25,000 |
$25,000 |
Title: The role of technology-enriched,
technology-mediated learning communities in reforming mathematics
teacher education
Summary:
This project examines the impact of a technology-enriched teacher
education program on beginning teachers' integration of educational
technologies into secondary institute mathematics classrooms. It seeks to
increase theoretical understanding of how beginning teachers are
initiated into a collaborative professional community featuring both
web-based and face to face interaction, and how participation in such
a community shapes their pedagogical beliefs and actions. Of central
interest is the role of technologically knowledgeable pre-service and
beginning teachers as agents ofinnovation and reform in secondary
institute mathematics. Outcomes will inform the design and implementation
of models of pre-service teacher education and professional
development.
Institution: The University of Queensland
A/Prof Mark Gould
Prof RJ Baxter
Prof VV Bazhanov
Dr PG Bouwknegt
Dr OE Foda
Dr PD Jarvis
Dr IN McArthur
A/Prof PA Pearce
|
2002 |
2003 |
2004 |
| Funding |
$157,836 |
$150,000 |
$150,000 |
Title: Algebraic Structures in Mathematical Physics
and Their Applications
Summary:
Algebraic structures such as affine (super)algebras, quantised
algebras and vertex operator algebras are among the most important
discoveries in mathematics. They provide a universal common algebraic
framework underlying applications in a wide range of physics
(eg. statistical mechanics, string theory, condensed matter physics
etc.) leading to a high level of research activity worldwide. The
project harnessess the high level of expertise in mathematical physics
across Australia to focus on exciting new developments in the theory
of these algebraic structures and their application to physics, thus
ensuring Australia plays a leading role in this rapidly expanding
field.
Institution: The University of Melbourne
Prof. Anthony Guttmann
Dr AL Owczarek
Dr R Brak
Dr I Jensen
|
2002 |
2003 |
2004 |
2005 |
2006 |
| Funding |
$130,000 |
$175,000 |
$175,000 |
$70,000 |
$70,000 |
Title: Advanced Computational and Analytic Studies in
Lattice Statistical Mechanics and Applications
Summary:
Lattice Statistical Mechanics is one of the current success stories of
Australian Science with a significant international presence. The
applicants represent a centre of excellence, particularly in the area
of combining computational and analytic studies for maximum scientific
benefit. The programme of research maximises Australia's investment in
this human resource by focussing on an integrated set of projects
comprising a diverse and innovative group of applications in areas
such as polymer science, DNA denaturation, combinatorics and the study
of traffic flows. The underlying theme is always the utility of
lattice statistical mechanics in 21st century science.
Institution: The Australian National University
Prof. Peter Hall
|
2002 |
2003 |
2004 |
2005 |
2006 |
| Funding |
$294,104 |
$294,104 |
$294,104 |
$70,669 |
$70,669 |
Title: Nonparametric Statistics
Summary:
Nonparametric statistical methods are techniques that implicitly
choose statistical models from exceptionally large and highly adaptive
classes. The project aims to develop innovative and practicable
nonparametric methods in four areas: Statistical Smoothing, Data
Mining, Mixture Methods and Robust Inference. The significance of the
work lies in its novelty, the breadth of its practical motivation, and
its position at the leading edge of contemporary work in
statistics. Expected outcomes include new technologies for data
analysis.
Institution: The University of Queensland
A/Prof George Havas
Dr DE Bryant
Dr P Adams
Prof. AP Street
|
2002 |
2003 |
2004 |
| Funding |
$90,000 |
$100,000 |
$100,000 |
Title: Emerging applications of advanced computational
methods and discrete mathematics.
Summary:
Ongoing improvements in computer performance are revolutionising
research in combinatorial discrete mathematics, and leading to
exciting new applications in information technology and the biological
and chemical sciences. As a result, substantial international research
effort, both at universities and in commercial and industrial
organisations, is being channelled into high-performance computation
and theoretical problems in combinatorial mathematics. Our aim is to
develop and apply advanced computational methods through the study of
several unsolved theoretical problems in design theory and practical
problems in exact matrix computation and drug design.
Institution: The University of Sydney
Prof. Nalini Joshi and Dr CM Cosgrove
|
2002 |
2003 |
2004 |
| Funding |
$55,000 |
$55,000 |
$55,000 |
Title: Singularities And Classifications Of Integrable
Systems
Summary:
What mathematical models of engineering and nature exclude chaos and
have globally predictable solutions? What models occur ubquitously in
fields as diverse as photonics and quantum gravity? The answers lie in
the theory of integrable systems. We aim to develop powerful new
algorithms for identifying integrable models and for deducing their
remarkable properties. These algorithms are expected to answer
fundamental questions of contemporary importance. Longer term possible
outcomes include applications to nonlinear optics and quantum
computing.
Institution: The University of Melbourne
Prof. Vikram Krishnamurthy
|
2002 |
2003 |
2004 |
2005 |
2006 |
| Funding |
$120,000 |
$130,000 |
$130,000 |
$63,084 |
$63,084 |
Title: Stochastic Sensor Scheduling in Statistical
Signal Processing
Summary:
In several statistical signal processing applications, due to
computational or communication constraints, at each time instant one
can use only a few out of several possible noisy (stochastic)
sensors. The stochastic sensor scheduling problem deals with how to
dynamically choose which group of sensors to pick at each time
instant. This project involves research in sensor scheduling for
widely used stochastic dynamical systems such as Hidden Markov Models
and Jump Markov Linear Systems. It focuses on the design and analysis
of stochastic control algorithms such as dynamic programming and
simulation based randomized methods. The research will lead to an
integrated theory incorporating stochastic control, statistical signal
processing and combinatorial optimization. We will also apply the
resulting techniques to tracking maneuvering targets given noisy
observations.
Institution: The Australian National University
Dr Denis Labutin
|
2002 |
2003 |
2004 |
| Funding |
$61,184 |
$62,967 |
$62,967 |
Title: Nonlinear Partial Differential Equations:
Singularities, Potential Theory, and Geometric Applications
Summary:
The main objective of the project is to study properties of solutions
to fully nonlinear, elliptic partial differential equations. Rather
than studying more traditional existence-uniqueness problems the main
task will be to investigate qualitative questions. These concern the
behaviour of solutions to the equations, the description of possible
pathologies and singularities the solutions can have, and conditions
for the absence of singularities. Understanding of the singular
behaviour of solutions is very important for applications in geometry,
physics, elasticity, and mechanics. From this point of view, probably
the most important problem is to find explicit information about
singularities of solutions.
Institution: The University of Sydney
Dr King Lai
|
2002 |
2003 |
2004 |
| Funding |
$50,000 |
$70,000 |
$70,000 |
Title: Representation theory of groups and
applications to geometry and number theory
Summary:
Representation theory is at the center of the mathematical study of
symmetry, which we constantly use to understand the world. Combine
with geometry this theory produces spectacular results in number
theory. This project aims to study p-adic phenomena in these
theories. Its main outcomes will be p-adic automorphic forms and local
functoriality.
Institution: Australian National University -
Institute of Advanced Studies
Prof Alan McIntosh
|
2002 |
2003 |
2004 |
| Funding |
$75,000 |
$119,000 |
$119,000 |
Title: Harmonic Analysis, Boundary Value Problems, and
Maxwell's Equations in Lipschitz Domains
Summary:
Boundary value problems for partial differential equations arise
naturally when physical problems are expressed in mathematical
terms. This project concerns the systematic development of the
harmonic analysis of partial differential operators, and of the
corresponding boundary integrals in order to solve such problems on
irregular regions. Particular emphasis is given to studying the
behaviour of electromagnetic waves both inside and outside irregularly
shaped surfaces, and their propagation through it.
Institution: The Australian National University
Prof. Brendan McKay
|
2002 |
2003 |
2004 |
2005 |
2006 |
| Funding |
$120,000 |
$130,000 |
$130,000 |
$66,831 |
$68,836 |
Title: Practical and theoretical aspects of structure
enumeration
Summary:
Many areas of study involve processing of large numbers of objects in
some class. These are countless examples in chemistry, physics,
mathematics, and other disciplines. Structure Enumeration is the study
of methods for efficient generation and analysis of such objects. The
project will involve exploitation and extension of recent advances,
many due to the CI, which have added orders of magnitude to what was
possible only a few years ago. The outcome will be a combination of
theoretical results and practical achievements, whose usefulness will
be demonstrated with some serious applications in physics and
mathematics.
Institution: The University of Western Australia
A/Prof Ross Maller and Prof. CC Klueppelberg
|
2002 |
2003 |
2004 |
| Funding |
$55,000 |
$60,000 |
$60,000 |
Title: Stochastic Analysis with a View to Applications
in Financial Risk Processes
Summary:
Recent decades have seen explosive growth in applications of
probability theory and statistics to the modelling of risk in finance
and insurance. An intensive theoretical investigation into passage
time and other problems for Levy and other continuous time processes
will be applied to financial risk analyses. Related investigations
will involve perpetuities and stochastic volatility models for price
series. Outcomes will include the development of new theory in
probability and statistics, the initiation and reinforcement of
collaborative ties with major international research figures, and the
fostering of contacts with the finance industry.
Institution: The University of Western Australia
Dr Alice Niemeyer and Prof. CE Praeger
|
2002 |
2003 |
2004 |
| Funding |
$62,000 |
$62,000 |
$62,000 |
Title: Group algorithms: Complexity, Theory and Practice.
Summary:
The symmetry of a mathematical or physical system is often best
described by an abstract structure called a group, and groups are
commonly represented as groups of permutations or matrices. In this
project we shall design and analyse a general algorithmic framework
for computing with finite groups. In the context of permutation groups
and matrix groups we will produce prototype implementations. The
proposed framework has the potential to revolutionise algorithmic
group theory as it draws together theoretical and computational models
of groups.
Institution: The University of New South Wales
A/Prof Liqun Qi
|
2002 |
2003 |
2004 |
| Funding |
$60,000 |
$75,000 |
$75,000 |
Title: Robust Reformulation Methods
Summary:
Many decision problems in engineering, business and economics are
modeled as nonlinear continuous optimization problems. Often these are
made difficult by the existence of constraints. In this project, we
reformulate such problems as constrained nonsmooth equations, rather
than optimization problems, and develop generalized Newton and
quasi-Newton methods for solving them. The expected outcomes of this
project include a systematic theory of reformulation methods, and
robust and efficient algorithms for solving some important nonlinear
continuous optimization problems. There is high potential for
applications in engineering, business and finance.
Institution: La Trobe University
A/Prof Gilles Quispel
A/Prof RI McLachlan
Prof A Iserles
Prof B Leimkuhler
Prof H Munthe-Kaas
Dr A Zanna
|
2002 |
2003 |
2004 |
| Funding |
$90,000 |
$70,000 |
$70,000 |
Title: Geometric Numerical Integration
Summary:
Many scientific phenomena in physics, astronomy, and chemistry, are
modelled by ordinary differential equations (ODEs). Often these
equations have no solution in closed form, and one relies on numerical
integration. Traditionally this is done using Runge-Kutta methods or
linear multistep methods. In the last decade, however, we (and others)
have discovered novel classes of so-called "geometric" numerical
integration methods that preserve qualititative features of certain
ODE's exactly (in contrast to traditional methods), leading to crucial
stability improvements. Extending concepts from dynamical systems
theory and traditional numerical ODEs, this project will improve,
extend and systematize this new field of geometric integration.
Institution: The University of Melbourne
Mr Andrew Rechnitzer
|
2002 |
2003 |
2004 |
2005 |
| Funding |
$49,888 |
$47,226 |
$47,226 |
$47,226 |
Title: Key combinatorial problems in lattice
statistical mechanics
Summary:
The enumeration of lattice animals is a famous open problem in
combinatorics. These discrete structures also underpin our
understanding of many physical phenomena, including polymer collapse
and percolation in random media, through the integral part they play
in many models in statistical mechanics and theoretical chemistry.
The project aims to answer some key open problems in this area using
exact and numerical techniques. We expect that this will lead to
proofs of the insolvability of certain problems, new exact solutions
of others, and a greater understanding of the effect of topology and
geometry on the behaviour of these models.
Institution: The University of Newcastle
Mr Adam Rennie
|
2002 |
2003 |
2004 |
| Funding |
$61,184 |
$62,967 |
$62,967 |
Title: New Directions in Noncommutative Geometry.
Summary:
A. Connes' noncommutative geometry has recently become important in
topology, geometry and physics. The central geometric objects in
noncommutative geometry are called spectral triples. Spectral triples
also provide the framework for studying some important classes of
equations. This project will extend the definitions of spectral
triples to cover additional important examples. This extension will
provide the tools to study a broad class of boundary value problems in
the theory of equations. Such problems occur in several areas of
modern physics. In addition, results obtained will be useful for
studying the structure of the most important spectral triples, called
noncommutative manifolds.
Institution: The University of Newcastle
A/Prof A Guyan Robertson
|
2002 |
2003 |
2004 |
| Funding |
$45,000 |
$51,000 |
$52,000 |
Title: Noncommutative geometry of groups acting on buildings
Summary:
Consider a tiling of the plane by triangles, where each triangle is
labeled by an element of a finite alphabet. Suppose that only certain
pairs of labels are allowed to be adjacent to each other in each
direction. The tiled planes can be pasted together to form the
abstract mathematical object known as a building. This building and
its boundary, give rise to new families of
C*-algebras and groups. The
algebras have a rich structure which it is proposed to investigate and
link with geometric properties of the groups. New insights into
geometry, dynamics and algebra are expected.
Institution: The University of Melbourne
Prof. Joachim Rubinstein
|
2002 |
2003 |
2004 |
2005 |
2006 |
| Funding |
$90,000 |
$131,000 |
$125,000 |
$60,000 |
$60,000 |
Title: Topics on 3- and 4-dimensional manifolds.
Summary:
- to develop practical algorithms for recognising surfaces, knots
and 3-dimensional spaces. These will be very useful for
experimentation and to understand the computational complexity of
such questions.
- to understand the properties of minimal surfac
Institution: The University of Newcastle
Dr Maria Seron and Prof. GC Goodwin
|
2002 |
2003 |
2004 |
2005 |
2006 |
| Funding |
$90,000 |
$120,000 |
$120,000 |
$78,601 |
$78,601 |
Title: Constrained Receding Horizon Control of Nonlinear Systems
Summary:
Most real world control problems involve the design of strategies that
achieve performance goals in the presence of constraints on the system
variables. Receding horizon control is a strategy that addresses this
problem by directly optimising performance under the appropriate
constraints. This project will address theoretical and computational
issues associated with this methodology. The expected outcomes
include:
- New finitely parameterised solutions for nonlinear systems.
- Implementations of reduced computational complexity.
- New insights into analytical properties of the methodology.
These outcomes are expected to add to Australian scientific
recognition and to bring significant economic benefit to Australian
industry.
Institution: Macquarie University
Dr Igor Shparlinski
|
2002 |
2003 |
2004 |
| Funding |
$70,000 |
$90,000 |
$90,000 |
Title: Number Theoretic Methods in Cryptography
Summary:
It is well known that Number Theory, besides its intrinsic beauty,
provides many powerful tools for modern Cryptography. The aim of the
project is to formulate and solve new and important mathematical
problems, which lie in the background of modern cryptography. They are
also of independent value for pure mathematics because they very often
stimulate new approaches to and new surprising points of view on
classical results and methods. The main outcome will be advancing our
theoretical knowledge about several major cryptosystems. The project
will extend and enrich the area of applications of mathematics to
cryptography and related areas.
Institution: Monash University
Dr Kate Smith and Mr T Kwok
|
2002 |
2003 |
2004 |
| Funding |
$80,000 |
$92,000 |
$62,967 |
Title: Realising the promise of neural networks for
practical optimisation: improving their efficiency and effectivess
through chaotic dynamics and hardware implementation
Summary:
Combinatorial optimisation problems such as transportation routing and
assembly-line scheduling are critical to the efficiency of many
industries, but their combinatorial explosion makes rapid solution
difficult. Neural networks (NNs) hold much potential for rapid
solution though hardware implementation, but we need to improve the
quality of their solutions before developing hardware. We have
previously shown that the rich dynamics of chaos can improve the
efficiency and effectiveness of NNs. We aim to develop new chaotic NN
models, rigorously evaluate them on industrially significant problems
such as those arising in manufacturing, logistics and
telecommunications, and demonstrate their speed through hardware
acceleration.
Institution: The University of Adelaide
Dr Daniel Stevenson
|
2002 |
2003 |
2004 |
| Funding |
$61,184 |
$62,967 |
$62,967 |
Title: Higher Line Bundles in Geometry and Physics
Summary:
This project seeks to develop a theory of geometric objects, `higher
line bundles', which realise elements of higher dimensional cohomology
groups. In particular this project will develop a theory of
differential geometry for these objects, allowing one to interpret
differential forms representing cohomology classes as the `curvature'
of a higher line bundle. This will have applications in quantum field
theory and string/brane theory.
Institution: The University of Adelaide
A/Prof Peter Taylor
Dr NG Bean
Dr DP Kroese
Dr PK Pollett
|
2002 |
2003 |
2004 |
| Funding |
$63,319 |
$60,205 |
$60,087 |
Title: Operator-Analytic Methods in Telecommunication Systems
Summary:
Many systems in information technology and telecommunications evolve
under conditions of uncertainty. In this context, mathematical
modelling is an essential component of the design process. We shall
provide techniques for analysing a class of mathematical models,
called operator-analytic models, which can be used to study many of
the above-mentioned systems, such as the Internet. This project will
deliver efficient numerical algorithms that will make possible
practical analysis of operator-analytic models.
Institution: The University of Adelaide
A/Prof Arunas Verbyla, Dr GK Smyth and Prof. PJ Diggle
|
2002 |
2003 |
2004 |
| Funding |
$63,204 |
$60,801 |
$62,445 |
Title: Modelling mean and dispersion using fixed and
random effects
Summary:
The aims of the project are to develop methods for joint mean and
dispersion modelling using fixed and random effects, in the
generalized linear models context and for Gaussian longitudinal
data. The significance is the more efficient, precise and appropriate
analysis of data arising from many areas of application. The expected
outcomes are therefore better methods of analysis, software to carry
the analyses out, and potentially important results in applications.
Institution: The University of New South Wales
Dr Norman Wildberger
|
2002 |
2003 |
2004 |
| Funding |
$30,000 |
$40,000 |
$40,000 |
Title: Harmonic analysis on Lie groups via hypergroup
convolution structures
Summary:
This project studies convolution structures for conjugacy classes of
nilpotent and compact Lie groups and the connections with fusion rule
algebras. The aims are to establish a suitable theory of almost
periodic functions on a nilpotent Lie group to allow a wrapping
theorem to be formulated, to describe precisely the class hypergroup
of a compact Lie group, and to clarify the relations of the latter
with fusion rule algebras. This will result in further understanding
of the Kirillov orbit method and the have applications to conformal
field theory.
Institution: The University of Newcastle
Dr George Willis and Dr J Ramagge
|
2002 |
2003 |
2004 |
| Funding |
$60,000 |
$60,000 |
$65,000 |
Title: Totally disconnected groups and their algebras
Summary:
Groups are algebraic objects which convey symmetry much as numbers
convey size. For example, the symmetries of a crystal form a
crystallographic group and the classification of crystallographic
groups describes all possible crystal structures. Totally disconnected
groups arise as symmetries of network structures having nodes and a
`neighbour' relation, as models of crystals do, but which are not
rigid like crystals. Powerful techniques for analysing totally
disconnected groups have recently been discovered and this project
aims to develop those techniques. The resulting significant advances
in the understanding of symmetry will extend the range of applications
of group theory.
Institution: The University of Melbourne
Dr Nicholas Wormald
|
2002 |
2003 |
2004 |
| Funding |
$50,000 |
$70,000 |
$70,000 |
Title: Random Structures and Asymptotics
Summary:
Discrete random structures have many uses in algorithms in computer
science (for instance, random networks modelling computer link-ups),
biology (for instance, random sequences modelling DNA) and
engineering. New techniques for studying these structures will lead to
powerful new results on their properties. The emphasis will be on the
behaviour of the random structures when their size becomes large. With
the advent of more powerful computing techniques, it is often the
large-scale behaviour which has relevance to the more diffucult
computations being undertaken. The results are also of potential
application to other areas of mathematics.
Institution: The University of Sydney
Dr Ruibin Zhang and Dr AI Molev
|
2002 |
2003 |
2004 |
| Funding |
$55,000 |
$75,000 |
$75,000 |
Title: Representations and Applications of Quantum Groups
Summary:
The theory of quantum groups originated from soluble lattice models in
statistical mechanics, but it turned out to have important
applications to a wide range of subjects in mathematics and
physics. For this reason, quantum groups have occupied a central stage
of international mathematical research for the last decade, and
continue to attract great interest. This project addresses some
important open problems on representations and applications of some
finite dimensional quantum groups.
