- Complete Integrability
Completely integrable partial differential equations, singularity analysis, Painlevé equations.
- Elliptic Partial Differential Equations (linear and nonlinear)
Effect of the underlying domain, isoperimetric inequalities, study of large solutions or solutions when the diffusion is small (and relation with finite Morse index solutions), topological methods.
- Mathematical Biosciences
The construction of mathematical models of biological systems is an important and rapidly expanding area of research. Such systems are very complex, but mathematics can serve to elucidate underlying principles and identify directions for experimental research. A strength of the biology group is the close contacts with experimental groups at Sydney; a very successful collaboration with the Department of Physiology has been in place for over 10 years, leading to the award of competitive research grants totalling over 1.25 million dollars. Current research topics include: social insects, biological pattern formation, communication in neurons and neural systems, synaptic function, autonomic nervous system, phylogenetics, biomedical ultrasound.
Researchers: C. Cosgrove, N. Dancer, D. Daners, W. Gibson, L. Farnell, G. Gottwald, N. Joshi, M. Myerscough, S. Santra, K. Wang.
Prof EN Dancer (N.Dancer@maths.usyd.edu.au)