Applied Mathematics Research Areas

• Dynamical Systems
• Financial Mathematics and Mathematical Economics
• Geophysical and Astrophysical Fluid Dynamics
• Industrial and Biomedical Modelling
• Integrable Systems
• Mathematical Biology

Contact person: A/Prof. C. Macaskill

Dynamical Systems

Nature is inherently nonlinear. Much of its complexity and beauty is reflected in the border between chaos and order. Here unexpected universal structures can lead to a deep understanding not only of nature but also of social systems.

Specific research areas: Hamiltonian dynamics, slow-fast systems, nonlinear waves, chaos, pattern formation, perturbation theory

Researchers: J. Atkinson, H. Dullin, G. Gottwald, N. Joshi, S. Olver, C. Macaskill, M. Wechselberger.

Financial Mathematics and Mathematical Economics

Modern Financial Mathematics is concerned with modelling financial markets, pricing derivatives contracts and understanding risk. These studies directly impact on banks and financial institutions worldwide.

Specific research areas: exotic options, interest rate derivatives, credit risk, stochastic volatitily, environmental economics, macroeconomic theory

Researchers: M. Rutkowski

Geophysical and Astrophysical Fluid Dynamics

The dynamics of planetary and stellar atmospheres and interiors is inherently complex, involving a vast range of spatial and temporal scales. This poses a great challenge for the analytical and computational treatment.

Specific research areas: nonlinear waves, numerical methods, dynamo theory, magnetohydrodynamics, atmospheric dynamics, data assimilation, vortex dynamics

Researchers: D. Galloway, G. Gottwald, D. Ivers, C. Macaskill.

Industrial and Biomedical Modelling

Applied mathematics has been successful in improving existing industrial processes and biomedical technologies, and creating new technologies. Modelling, simulating and desiging novel technologies can help reduce cost and increase efficiency.

Specific research areas: biomedical ultrasound, manufacturing optical fibres, genetic algorithms for design and optimisation.

Researchers: C. Macaskill, L. Poladian, R. Thompson, F. Viera.

Integrable Systems

The theory of integrable systems ranges widely in mathematics and physics. The study of integrable systems unveils intriguing and beautiful geometrical and topological aspects of fundamental equations, often with surprising applications.

Specific research areas: discrete integrable systems, Painlevé equations, (quantum) monodromy, soliton equations, topology of integrable systems, Riemann-Hilbert problems

Researchers: J. Atkinson, C. Cosgrove, C. Cresswell, H. Dullin, N. Joshi, S. Olver

Mathematical Biology

The construction of mathematical models of biological systems is an important and rapidly expanding area of research. A strength of the group are the close contacts with experimentalists at Sydney and overseas.

Specific research areas: neurophysiology, physiological rhythms, collective behaviour, cardiac dynamics, biomechanics, cancer, immunology

Researchers: H. Dullin, L. Farnell, G. Gottwald, N. Joshi, P. Kim, M. Myerscough, L. Poladian, R. Thompson, M. Wechselberger.