Institute for Mathematics & its Applications
about imia
research
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Some members of IMIA
From left (back two rows): Ashraf Allehaib... |
Members
- Dr Nathan Brownlowe
- Dr Joanna Goard
- Prof Tim Marchant
- Dr James McCoy
- Dr Mark Nelson
- A/Prof Peter Nickolas
- A/Prof David Pask
- Prof Jacqui Ramagge
- Dr David Robertson
- Dr Aidan Sims
- Dr Ngamta Thamwattana
- Dr Samuel B.G. Webster
- Dr Michael Whittaker
- Dr Annette Worthy
- Prof Song-Ping Zhu
Biographies
Dr Nathan Brownlowe 
Nathan Brownlowe completed his undergraduate studies in 2001 at the University of Newcastle, Australia. He completed his PhD in pure mathematics in 2006 under the supervision of Iain Raeburn at the University of Newcastle. After a couple of years away from academia, Nathan became a Research Fellow in 2008 at the University of Wollongong, working on an ARC grant with Iain Raeburn (UOW) and Astrid an Huef of the University of New South Wales. Nathan's research interests lie in the area of operator algebras. Specifically, he studies the C*-algebras associated to various mathematical objects such as dynamical systems, directed graphs and their higher-rank analogues, and Hilbert bimodules.
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Dr Joanna Goard 
Joanna worked for a short time at BHP as a systems engineer before undertaking a lectureship at UoW. She received her doctorate in Applied Mathematics in 1998 with a thesis entitled ‘Symmetry and Ad-hoc Methods for Solving Nonlinear Differential Equations’. Since then her two main areas of research interest are:
- generalized symmetry methods for solving PDEs. To a large extent our understanding of the fundamental processes from the natural and business worlds is based on partial differential equations (PDEs) which arise from mathematical modelling. Joanna works to extend symmetry solution techniques so that many more solutions of previously unsolvable problems in finance and the physical world can be found.
- the mathematics of financial derivatives. Joanna studies the relationship between stochastic differential equations for underlying variables such as interest rates, volatility and stocks and the partial differential equations governing prices of financial derivatives such as bonds, options and volatility contracts. Joanna has also worked with problems dealing with incomplete markets. She has priced defaultable bonds by incorporating inherent risks with the use of utility functions. The approach achieved exact solutions even when the default probability parameter was itself a stochastic variable.
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Prof Tim Marchant 
Prof. Marchant is Dean of Research at UOW and a Professor of Applied Mathematics. He is currently Chair of ANZIAM, the Society for Australian and NZ Industrial and Applied Mathematics. He is a member of a DEEWR Endeavour Scholarships panel and was Director of the Mathematics and Statistics in Industry Study Group (MISG), 2007-9.
He gained a PhD in Applied Mathematics from the University of Adelaide in 1988, has published 60 research papers and successfully supervised ten research students on various topics in Applied Mathematics. His ISI citation summary shows 54 articles, with 315 citations and a Hirsch factor of H=9.
His research areas cover a diverse range of areas, including nonlinear waves and optics, and combustion theory. A key focus of his research is the development of accurate approximate solutions to partial differential equations. Some recently studied topics include the propagation of solitary waves in nematic liquid crystals, solitary wave evolution and interaction for higher-order versions of integrable equations, and accurate semi-analytical solutions for reaction-diffusion equations.
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Dr James McCoy 
James is a 'geometric analyst' whose main research interests are questions related to nonlinear curvature driven heat-type flows of hypersurfaces. Such questions include long time existence of globally constrained curvature flows, formation of singularities (where the curvature becomes unbounded) in curvature flows and extension of classical flow solutions beyond singularities using a 'surgery' procedure. Such analysis relies heavily on techniques from differential geometry, elliptic and parabolic partial differential equations, functional analysis and topology.
James is also interested in geometric analysis of problems in biology, including the shapes of proteins and blood cells.
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Dr Mark Nelson 
Mark’s general area of interest is in non-linear chemical dynamics. His research involves the application of bifurcation theory, continuation methods, dynamical systems methodology and singularity theory to practical problems arising in areas such as physical chemistry, bioreactor engineering, chemical reactor engineering, combustion and fire engineering. Currently he is working on problems in the following areas.
- Combustion (including combustion of polymeric materials and spontaneous ignition of compost)
- Heterogeneously catalysed combustion
- Bioreactor engineering
- Chemical reactor engineering
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A/Prof Peter Nickolas 
Peter has research interests which are concentrated mainly in topological algebra and the geometry of metric spaces, though they branch at times also into pure algebra, topology and theoretical computer science.
In topological algebra, his interests are focused in the area of topological groups, but are largely outside of the traditional domain of harmonic analysis and instead deal with groups that are in some sense "large" or "general". A substantial continuing theme in his work has been the theory of free topological groups and free products of topological groups.
In metric spaces, he works especially on connections between the geometry of the spaces and certain associated spaces of measures and spaces of functions.
Peter has continuing collaborative research projects with colleagues at several overseas institutions.
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A/Prof David Pask 
- Operator Algebra: David’s primary interest is in a field of Pure Mathematics called Operator Algebra. Operator algebras were first formulated in the 1930’s as Mathematicians began to formalise quantum mechanics. Since then operator algebras have played a role in many areas of Mathematics and theoretical Physics.
Specifically, David is interested in the operator algebras generated by operators which satisfy relations encoded by a directed graph. His work has shown that many properties of the operator algebra can be read off from properties of the directed graph. There are also interesting connections with combinatorial topology and nonabelian duality. Lately, I have been working on higher dimensional versions of directed graphs, called k-graphs, which contain much more information and provide the potential for new applications. - Dynamical Systems: David has a secondary, but nonetheless important interest in an area of Dynamical Systems called Symbolic Dynamics. Symbolic dynamical systems provide models for many dynamical systems and have applications in Statistics, Computing and Coding theory. From David’s point of view, symbolic dynamical systems are interesting as they may be modeled by the paths in a directed graph and so have an important connection with my work in Operator Algebra. His work has shown that there are strong connections between the dynamical properties of the systems modeled by a directed graph and the algebraic properties of the operator algebra associated to the directed graph. Lately, David has been interested in dynamical systems modeled by a labeled directed graph, such systems are much more complicated as one can give many different edges in a graph the same label.
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Prof Jacqui Ramagge 
Jacqui Ramagge has broad expertise in pure mathematics and its applications, with publications in the areas of algebra, analysis and control theory. She is particularly interested in the structure theory of totally disconnected, locally compact groups (including Kac-Moody groups over local fields) and operator algebras (including von Neumann algebras and C*-algebras). She is a member of the Engineering, Mathematics and Informatics panel of the Australian Research Council College of Experts. She is on the Council of the Australian Mathematics Society and an editor of the Australian Mathematics Lecture Series.
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Dr David Robertson 
David Robertson received a bachelor of mathematics with first class honours from the University of Newcastle in 2006. He began studying towards his Ph.D in 2007 under the supervision of Wojciech Szymanski. In 2008 moved to the University of Southern Denmark to complete his studies, and graduated in November 2011. He is currently employed as a research fellow under the supervision of Aidan Sims.
David's primary research interests are in operator algebras, in particular, C*-algebras associated to Hilbert bimodules and higher rank generalisations. The theory of C*-algebras was originally developed as a formalisation of quantum mechanics, where observables of a physical system - quantities we can measure - can be represented as particular elements of a C*-algebra. Since then, the general theory of C*-algebras has been well developed and applied to many other areas of mathematics such as geometry and number theory. The benefit of associating C*-algebras to Hilbert bimodules is that certain structural properties of the C*-algebra important in classification may be formulated in terms of the underlying bimodule, which simplifies many calculations.
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Dr Aidan Sims 
Aidan Sims received a Bachelor of Computer Science and a Bachelor of Mathematics with First Class Honours and a University Medal in Mathematics at the University of Newcastle, Australia in 2001. In 2001, he undertook a PhD at the same institution, incorporating a six-month research exchange to the University of Iowa. His PhD was conferred in 2004. He took a post-doc funded by the ARC Centre of Excellend in Complex Dynamic Systems and Control at Newcastle in 2004, and was awarded an Australian Postdoctoral Fellowship in 2005. In 2007 he moved to the University of Wollongong to commence a permanent position, and was promoted to Senior Lecturer in 2010.
Aidan’s research is in operator algebras, particularly those associated to directed graphs and to Hilbert bimodules. His results have largely been concerned with uniqueness theorems, simplicity and classifiability for such algebras. Recently, however, he has begun work on a new approach to the theory based on so-called co-universal properties. He has also recently been working in the area of operator algebras associated to groupoids. He has on a number of occasions been invited to present his work at major specialist conferences in the US, Italy, Malaysia and Norway.
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Dr Ngamta Thamwattana 
Ngamta Thamwattana (Natalie) received a Bachelor of Science with First Class Honours in Mathematics at Mahidol University, Thailand, in 2000. In 2001, she undertook her PhD in Applied Mathematics at the University of Wollongong, Australia and graduated in 2005. Her PhD focused on the mechanics of granular materials. She is now working in nanomechanical areas to develop new mathematical models, which can be used for improving and developing nanotechnology. Her main research areas include electrorheological fluids and the mechanics of nanostructures. In 2007 she was awarded an Australian Postdoctoral Fellowship from the Australian Research Council to develop mathematical models for applications of nanomaterials in biology and medicine. She has made many contributions to the analysis of the mechanical characteristics of using nanotubes as nanocarriers for targeted drug delivery. This work in particular involves exact mathematical formulae for the potential energy and the interaction forces between various nanostructures. These results give precise predictions for the equilibrium spacing of the two molecules and the conditions under which a molecule will be attracted into or repulsed from a particular nanotube. She has also undertaken research on predicting the structure of proteins, where she has adopted the framework of the calculus of variations to study the protein folding problem with an energy functional dependent on the curvature, torsion and their derivatives with respect to the arc length of the protein backbone. Minimizing this energy amongst smooth normal variations yields two Euler-Lagrange equations, which are correctly derived for the first time. Further, these equations are also used to provide correct numerical constants which are suitable for explaining the physical behaviour of several types of DNA. Currently, she is developing a mathematical model to assess toxicology and health hazards of nanoparticles.
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Dr Samuel B.G. Webster 
Samuel Webster was born in 1985 in Albury, Australia. He completed high school in East Maitland. He received his Bachelor of Mathematics with First Class Honours from the University of Newcastle in 2006. He studied toward his PhD under the supervision of Iain Raeburn and Aidan Sims from 2007 in Newcastle. He moved to the University of Wollongong in 2007 to complete his studies, and received his PhD in 2011. He is currently a Research Fellow on an ARC grant held by David Pask.
Samuel's research interests include operator algebra and symbolic dynamics. Operator algebra is an exciting new field of research for pure mathematicians and theoretical physicists alike, originally developed as a formalisation for quantum mechanics roughly 80 years ago. Symbolic dynamical systems can model discrete processes such as computing and coding theory. Samuel is interested in symbolic dynamics through its links to operator algebra; many symbolic dynamical systems can be thought of as directed graphs, to each of which we can associate an operator algebra in such a way that that properties of the algebra can be read straight from a picture of the graph.
Samuel's current research focus is on graphical constructions and how they affect a graph's shift space and associated operator algebras. For example the Drinen-Tomforde desingularisation is a manipulation of a graph that changes some complicated graphs into simpler graphs without significantly affecting the associated shift spaces or operator algebras. Such constructions arise naturally as conjugacy or flow-equivalence on shift spaces. He is currently investigating multidimensional analogues of such constructions.
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Dr Michael Whittaker 
Michael Whittaker completed his doctoral studies in 2010 at the University of Victoria, Canada under the supervision of Ian Putnam.
Michael is currently employed as a research fellow on an ARC grant held by Iain Raeburn and Jacqui Ramagge. Michael's research is a combination of operator algebras and dynamical systems. In particular, he use techniques from noncommutative geometry and C*-algebras to understand hyperbolic dynamical systems known as Smale Spaces. On one hand, Smale spaces give rise to very interesting C*-algebras with particularly nice intrinsic properties that come from the hyperbolic structure of the Smale Space. On the other hand, C*-algebras come equipped with invariants which reveal information about the Smale Space in a noncommutative framework.
Michael is the IMIA seminar convener. Please get in touch with him if you would like to speak at the IMIA seminar.
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Dr Annette Worthy
- The development of mathematical techniques which enable the propagation of signals in optical fibres to be described with a high degree of accuracy.
- The development and implementation of computer aided learning (CAL) modules and mathematical engineering projects for engineering students enrolled in mathematics.
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Prof Song-Ping Zhu 
Song-Ping Zhu is a Professor of Applied Mathematics at the University of Wollongong, Australia. He graduated from the University of Michigan (Ann Arbor, Michigan, U.S.A.) with a PhD degree in December, 1987. He joined the School of Mathematics and Applied Statistics of University of Wollongong in 1991 as a Lecturer. He became an associate professor in 1997 and a full professor in 2007.
Professor Zhu’s work has been recognized internationally. He has published over 100 papers in international journals and conference proceedings and attracted funding supports from ARC (Australian Research Council) and private industries with accumulative sum over $1.1 Millions. Professor Zhu has established expertise in three major research areas:
- Financial Mathematics;
- Computational Mathematics and Numerical Methods for PDEs;
- Fluid Mechanics and Nonlinear Wave Theory.
But, his current research interests are on financial mathematics (option pricing with stochastic volatility models) and mathematical modeling in the area of renewable ocean wave energy.
Professor Zhu has ample experience in supervising PhD and research Masters students. He has successfully supervised five Ph.D students and six research Masters students to their graduation. All his five former PhD students gained employment overseas (USA, UK, and China, Malaysia and Thailand) right after their completion.
Currently Professor Zhu is on the editorial board of four international journals. He is also the Director of the Center of Financial Mathematics (CFM) and the Director of Institute of Mathematics and Its Applications (IMIA) at the University of Wollongong.
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Member Profile
Song-Ping Zhu graduated from the University of Michigan (Ann Arbor) with a PhD in 1987 and came to UoW in 1991. His current research interests are on financial mathematics (option pricing with stochastic volatility models) and mathematical modeling in the area of renewable ocean wave energy. [read more]
