Department of Mathematics
Division of Information and Communication Sciences
Macquarie University - Sydney
Current Research
The major research interests in the Mathematics discipline
are in number theory, functional analysis and partial
differential equations, category theory, harmonic analysis
and mathematical physics.
The follwing is a list of the broad research areas in the
department and the academic staff associated with them:
Functional Analysis, Harmonic Analysis, Partial Differential
Equations
- Dr. Bonnington M. N. Clarke: Control theory, hyperbolic partial
differential equations, boundary controllability and observability
of linear systems of partial differential equations, hyperbolic
differential boundary equations.
- Dr. Xuan Thinh Duong: Harmonic analysis and
partial differential equations.
- Dr. Christopher Meaney: Harmonic analysis on
Lie groups and symmetric spaces.
Number Theory and its Applications
- Dr. William W.L. Chen: Irregularities of distributions.
- Professor John H. Loxton: Number theory. Analytic number theory,
exponential sums, transcendental number theory, diophantine
approximation, applications to combinatorics, cryptography and
theoretical computer science.
- Dr. Gerald Myerson: Number theory. Finite fields, multivariate
polynomials, uniform distribution modulo one, Dedekind sums,
covering congruences, magic squares.
- Professor Alf J. Van der Poorten: Number theory,
theory of functions,
p-adic analysis. Transcendence theory, diophantine approximation,
diophantine equations, application of computers in number theory,
approximation of functions, value distribution of functions, p-adic
methods in number theory.
- Dr. Igor Shparlinski:
Number theory. Finite fields, computational number theory, application of
number theory to computer science and complexity of computations.
- Dr. Rodney I. Yager: Algebraic number theory. Arithmetic of elliptic
curves, Abelian varities, Iwasawa theory, p-adic L-functions and their
relationship to arithmetic properties of the associated variety.
Category Theory
- Dr. Michael S. J. Johnson
: Category theory. Applications of category
theory to computer science, homotopy theory and universal algebra.
- Professor Ross H. Street: Category theory and its application to algebraic
topology, homotopy theory, knots, combinatorics, group representations
and computer science.
- Dr. Dominic Verity: Higher-dimensional category theory and
its applications to simplicial/cubical geometries, homotopy theory,
non-abelian cohomology, category theory and sheaf representations of rings.
Algebra
Mathematical Physics
- Associate Professor John V. Corbett:
Mathematical aspects of quantum
theory, non-statistical interpretations of quantum theory that use
intuitionistic logic. Theory of measurement and Bell's inequalities.
Algebraic Geometry, Mathematical Computing and Typesetting
- Dr. Ross R. Moore: Algebraic geometry,
mathematical computing, mathematical typesetting and electronic presentation.
Cohomology of vector bundles over projective spaces, Horrocks-Mumford vector bundle.
Mathematical computer graphics, computational number theory, chaos, tilings and curves.
ross@maths.mq.edu.au, July 16, 2001