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About M&S
Students
Research
Staff
Organisational Unit
La Trobe University
Victoria 3086
AUSTRALIA
Tel: +61 3 9479 2600
Fax: +61 3 9479 2466
Email: mathstats-enquiries
@latrobe.edu.au
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Department of Mathematics and Statistics
Staff Research Interests
Staff Members and their Research Interests
Please note that, before you apply for admission or for a scholarship, you should contact the staff member whose interests are close to yours and who could therefore act as your supervisor. Below is a list of members of the Department of Mathematics. Under their names is a brief description of present research interests or of projects in which the staff member has recently been involved. This is intended to help potential applicants build a picture of the research culture of the Department. Actual research topics for new graduate students are a matter of negotiation between the applicant and the proposed supervisor.
Emeritus Scholar
Alan Andrew, MSc(NZ), MSc(ANU), PhD(La Trobe), FIMA, FAustMS.
Email: A.Andrew@latrobe.edu.au
- Development and analysis of methods, especially the method of asymptotic correction, for the efficient numerical computation of higher Sturm-Liouville eigenvalues and for the numerical solution of inverse Sturm-Liouville problems. Numerical computation of derivatives of repeated eigenvalues and the corresponding eigenvectors of matrix-valued functions.
Professors
Reinout Quispel, MSc, DipEd (Utrecht), PhD (Leiden).
Email: R.Quispel@latrobe.edu.au
- Dynamical systems: from chaos theory on the one hand, to the theory of integrable (i.e. completely ordered) systems on the other. Scientific computing: in particular "geometric numerical integration" of differential equations. Mathematical biology: in particular population dynamics.
- Statistical mechanics of charged systems. Chaotic dynamics of few-particle charged systems. Numerical simulation of the Brownian motion of the particles of a dense suspension. Parallel computation in simulations of all of the above.
Readers and Associate Professors
Grant Cairns, BE, BSc, MScSt (QLD), Doc 3e Cycle, Doc d'Etat (Montpellier).
Email: G.Cairns@latrobe.edu.au
- Differential geometry, particularly group actions, Lie algebra cohomology, invariants of curves and surfaces, and foliation theory.
Brian A. Davey, MSc (Mon), PhD. (Manit) FAustMS.
Email: B.Davey@latrobe.edu.au
- "General algebra (also known as universal algebra) and lattice theory. Interconnections between general algebra and constraint satisfaction problems in theoretical computer science. Algebraic aspects of the topological representation of algebras with particular emphasis on duality theory. Applications of duality theory to algebras with an underlying distributive lattice structure."
Geoff E. Prince, BSc, DipEd (Mon), PhD., FAustMS.
Email: G.Prince@latrobe.edu.au
- Applied differential geometry: in particular the use of tangent bundle techniques and exterior differential systems theory in the study of differential equations arising in mathematics and mathematical physics. Current topics include the inverse problem in the calculus of variations, congruence collapse in second order ordinary differential equations, and geometric reduction of order of partial differential equations.
Peter J. Stacey, MA (Camb), MSc, DPhil (Oxf).
Email: P.Stacey@latrobe.edu.au
- Algebras of operators on Hilbert spaces: C*-algebras, automorphisms, antiautomorphisms, endomorphisms, non-commutative dynamical systems, crossed products.
Simon J. Smith, BSc (Hons) (Tas), PhD (NE).
Email: S.Smith@latrobe.edu.au
- Approximation theory, particularly polynomial interpolation.
Inequalities.
- Frequentist confidence intervals and prediction intervals utilizing
uncertain prior information. The effect of preliminary model selection
on confidence intervals and prediction intervals. Exact confidence
intervals from count data. Time series prediction intervals that account
for parameter estimation errors.
Senior Lecturers
- Statistical mechanics; in particular exactly solvable models, and their connections with conformal field theory. The small-world phenomenon.
- Graph theory: in particular longest paths, labelling, flows, and
applications to demography and social networks.
Lecturers
- Topological dynamics generally and discrete topological dynamics in particular. Relationships between topological and metric 'chaos' type conditions. Chaotic maps on hyperspaces of a topological space. Iterated function schemes and fractal image compression.
- Universal algebra and the algebraic theory of semigroups. Special interests within these areas include: finite axiomatisability problems (varieties and quasivarieties); applications of general algebra to constraint satisfaction problems; applications of semigroups and algebras of functions and relations to the formal study of algorithms; and issues of computational complexity and decidability.
David McLaren, BSc (Hons)(Melb), PhD (Sussex).
Email: D.McLaren@latrobe.edu.au
- Algebraic aspects of the topological representation of algebras with emphasis on duality theory and standardness problems.
- Universal algebra, particularly natural duality theory and applications
of Priestley duality.
John W. Schutz, BE, BSc (Melb), PhD (Mon)
Email: j.schutz@latrobe.edu.au
- Axiomatic systems for space-times and geometries. Fluctuations of the electromagnetic field. Foundations of mechanics: relativistic and classical, dynamics of the electron.
- Theory and statistics of random fields. Spatial statistics. Sampling in
Fourier and signal analysis. Probability metrics. Stochastic in finance,
insurance and wireless communications.
Rob Champion, BSc (Hons) (Monash), DipEd (Monash), PhD (Monash).
Email:r.champion@latrobe.edu.au
- Applications of mathematics and statistics in health care
Ajay Chandra, BA(Fiji), PGD(Fiji), ME(Osaka), PhD(Osaka).
Email: A.Chandra@latrobe.edu.au
- Inference for GARCH and related time series; Multivariate analysis and
nonparametrics.
Associate Lecturers
- Chaos. Geometry of convex surfaces.
- Dimension Reduction techniques of high dimensional data
Research Fellows
Will Wright, BSc(Hons), MSc, PhD (Auck).
Email:W.Wright@latrobe.edu.au
- Numerical analysis of partial and ordinary differential equations. In particular, the efficient computation of problems using exponential or geometric integrators. Recently, I have started working on financial mathematics.
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