# Applied Mathematics Research Areas

- Computational Mathematics
- Dynamical Systems
- Financial Mathematics
- Geophysical and Astrophysical Fluid Dynamics
- Integrable Systems
- Mathematical Biology

**Contact person:** Prof. N. Joshi

## Computational Mathematics

Computational Mathematics occupies an important growing role at the intersection of theoretical and experimental science by designing efficient algorithms for processing large amounts of data and finding new ways to interpret complex patterns.

**Specific research areas:** spectral methods, agent-based modeling, high-performance supercomputing, multi-scale modelling, Riemann-Hilbert problems, random matrices, stiff time-integration

**Researchers:**
G. Gottwald,
D. Ivers,
P. Kim,
S. Olver,
G. Vasil

## 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, mathematical billiards

**Researchers:**
E. Altmann,
H. Dullin,
G. Gottwald,
N. Joshi,
S. Olver,
R. Marangell,
M. Radnovic,
G. Vasil,
M. Wechselberger

## Financial Mathematics

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.

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

**Researchers:**
B. Goldys,
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:**
G. Gottwald,
D. Ivers,
G. Vasil

## 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, geometry and topology of integrable systems, Painlevé equations, (quantum) monodromy, soliton equations, Riemann-Hilbert problems

**Researchers:**
C. Cresswell,
H. Dullin,
N. Joshi,
C. Lustri,
N. Nakazono,
S. Olver,
M. Radnovic,
Y. Shi

## 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:**
C. Bertram,
H. Dullin,
G. Gottwald,
N. Joshi,
P. Kim,
M. Myerscough,
L. Poladian,
R. Marangell,
M. Wechselberger