Department of Mathematics
RESEARCH IN MATHEMATICS
Research Groups in the Mathematics Department
To find more about the research interests of individual staff members, please click here.
Analysis
The research interests of the Analysis Group span functional analysis, harmonic analysis, Lie groups, symmetric spaces, partial differential equations and control theory. Some of the problems studied are mathematical formulations of physical situations and the solutions provided have applications to real world problems. For example, wavelet analysis is recognized as a significant advance in signal processing and compression. Similarly, answers to control theoretic questions at the quantum level are essential to realize the potential of the coming generation of computing devices. Members of the Analysis Group enjoy extensive research interaction and collaboration, nationally and internationally, and attract many overseas visitors to Macquarie University. They also receive many invitations to be speakers and main speakers at national and international conferences and workshops.
Category Theory
The Australian Category Seminar meets weekly at Macquarie University. The seminar includes staff and students from Macquarie University, the University of Sydney, the University of Western Sydney and the University of Technology, Sydney, as well as frequent visitors.
The Centre of Australian Category Theory (CoACT) was formed to provide the environment for the top international centre for higher-dimensional category theory and a major international centre for general category theory. It continues to pursue vigorously research into those parts of mathematics and computer science which find natural expression and advancement in terms of category theory and to train research students of the highest quality. It pursues the development of algebra of widespread applicability for the synthesis and analysis of systems and processes in fields as diverse as physics and computer science, and also mathematics itself. Although having operated as a coherent group since the founding of the ongoing Australian Category Seminar in 1971, CoACT was formally established in 1999.
The Scott Johnson Memorial Scholarship is available for full-time PhD studies at the Centre of Australian Category Theory at Macquarie University. Applicants should hold a First Class Honours degree in an appropriate field and be eligible for admission to the degree of Doctor of Philosophy in the Faculty of Science in the area of Mathematics. Entry details and application forms are available from the Higher Degree Research Unit.
Number Theory
The Number Theory Group has interests in many of the areas of modern number theory, including uniform distribution and discrepancy theory which have links with many other areas of mathematics such as analysis, algebra, probability theory, geometry and discrete mathematics.
The Number Theory Group has links with the Centre for Advanced Computing - Algorithms and Cryptography (ACAC) in the Department of Computing.
Applied Mathematics
Applied mathematics is a research area of increasing importance in the Department of Mathematics. The Applied Mathematics Group has interests in wave scattering and imaging, nonlinear dynamics, mechanics and geometry, and the work spans the areas of theoretical modelling, computational modelling and applications, including industrial applications as well as the theoretical development of the mathematical framework of large classes of models. Particular interests include
Members of the Applied Mathematics Group form part of a University Research Innovation funded team on inverse scattering, remote sensing and data inversion, a consortium of applied mathematicians, electrical engineers and geologists drawn from Macquarie University and the CSIRO. The Applied Mathematics Group has a strong international reputation that is built on significant interactions with other mathematicians, scientists and engineers, in Australia and internationally, and is demonstrated by its work with scientific and industrial organisations, such as the DSTO and the CSIRO, and their overseas counterparts.