Global Utilities

La Trobe University
Department of Mathematics and Statistics

Our research

The Department of Mathematics and Statistics has a very active research focus. We are recognised by the University as an area of research strength, with many national and international connections. Additionally our postdoctoral program supports our research program through national and international competitive grants. Our current research interests are listed below.

Mathematics

Dynamical systems, chaotic and integrable systems, numerical methods, differential geometry, general algebra, noncommutative dynamical systems, approximation theory, statistical mechanics, graph theory, topological dynamics.

Statistics

Theory of statistical inference, statistical modelling, dimension reduction, exact confidence intervals from count data, robust statistics, time series analysis, foundations of statistical inference, biostatistics.

Research groups

Staff research interests

Professors

  • Brian A. Davey
    • Universal algebra and lattice theory: topological representation of algebras, with particular emphasis on natural duality theory; applications of duality theory to algebras with an underlying distributive lattice structure.
  • Reinout Quispel
    • Dynamical systems: from chaos theory to integrable systems. Scientific computing: in particular, the “geometric numerical integration” of differential equations. Applied mathematics: traffic problems and mathematical biology.

Readers and Associate Professors

  • Grant Cairns
    • Differential geometry, particularly the dynamics of group actions, Lie algebra cohomology, topological graph theory and combinatorial game theory.
  • Paul Kabaila
    • Statistical inference: Frequentist confidence intervals and prediction intervals utilizing uncertain prior information. The effect of preliminary model selection on confidence intervals. Prediction intervals for time series.
  • Geoff Prince
    • Applied differential geometry: in particular, the use of jet bundle techniques and exterior differential systems in the study of differential equations arising in mathematics and mathematical physics.
  • John W. Schutz
    • Axiomatic systems for space-times and geometries.  Fluctuations of the electromagnetic field.  Foundations of mechanics: relativistic and classical, dynamics of the electron.
  • Katherine Seaton
    • Statistical mechanics: in particular, exactly solvable models and their connections with conformal field theory. The small-world phenomenon.
  • Simon J. Smith
    • Approximation theory, particularly polynomial interpolation. Inequalities.

Emeritus Professors

  • Terry Mills
    • Mathematical models in health care especially cancer services. Mathematical analysis, probability, statistics, history of ancient mathematics, graph theory.
  • Bert Mond
    • Nonlinear Programming, Generalized Convexity and Inequalities.
  • Robert Staudte
    • Statistical inference: in particular, distribution-free and robust statistics, and the foundations of statistics with applications to meta-analysis.

Emeritus Scholars

  • Alan Andrew
    • 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.
  • Peter J. Stacey
    • Algebras of operators on Hilbert spaces: C*-algebras, automorphisms, antiautomorphisms, endomorphisms, non-commutative dynamical systems, crossed products.

Senior Lecturers

  • Graeme Byrne
    • Spatial analysis of population mobility focusing on statistical models of Australian internal migration and commuting patterns.
  • Rob Champion
    • Applications of mathematics and statistics in health care.
  • Marcel Jackson
    • Universal algebra and semigroups: computational complexity and decidability; finite axiomatisability problems; constraint satisfaction problems; applying algebras of functions and relations to the formal study of algorithms.
  • Christopher Lenard
    • Graph theory: in particular longest paths, labelling, flows, and applications to demography and social networks.
  • Andriy Olenko
    • Probability and statistics: theory and statistics of random fields; spatial statistics; sampling in Fourier and signal analysis; probability metrics; stochastic in finance, insurance and wireless communications.
  • Luke Prendergast
    • Robust statistics and dimension reduction: Influence function analysis of statistical methods; theory and application of dimension reduction methods for the analysis of high dimensional data with an emphasis on visualization.

Lecturers

  • John Banks
    • Discrete time topological dynamics with a focus on relationships between topological and metric 'chaos'. Symbolic dynamics and its relation to formal language theory.
  • Yuri Nikolayevsky

    • Riemannian geometry, geometry of submanifolds, integral and conformal geometry. Lie groups and Lie algebras, homogeneous spaces and symmetric spaces. Topological graph theory.

  • Narwin Perkal

    • Algebraic aspects of the topological representation of algebras with emphasis on duality theory and standardness problems.

Associate Lecturers

  • Mitra Jazayeri
    • Dimension Reduction techniques of high dimensional data.

Research Fellows

  • Peter van der Kamp
    • Integrable systems and their connections with number theory, geometry and combinatorics. Symmetries of partial differential equations. Integrals and algebraic entropy of mappings.
  • Jane Pitkethly
    • Universal algebra, particularly natural duality theory and applications of Priestley duality.

Honorary Staff

For Current Students

For Staff