# Research Group Applied Mathematics

The research group Applied Mathematics belongs to the department of Mathematics and Computer Science of the University of Antwerp, Belgium. The research group develops numerical and mathematical methods for large scale simulations with applications in scientific, financial and industrial problems. These methods make it possible to study models with multiple variables in many dimensions, and in their full complexity.

### Financial mathematics

In the past decennia the international financial markets are witnessing a huge increase in the trading of more and more complex products, such as exotic options and interest rate products, and this growth is only amplifying. For the traders it is of crucial importance to be able to price these products accurately, robustly, and as fast as possible. In contemporary models, the prices of options are described as solutions to multi-dimensional and time-dependent partial differential equations, constituting extensions to the celebrated one-dimensional Black-Scholes equation. In our research we design and analyze numerical techniques that can effectively solve these large-scale equations.

### Mathematical methods for physics, biology and chemistry

In physics and chemistry experimental tools are now able to probe the dynamics inside molecules and solids. To accurately predict the outcome of these experiments mathematical tools are needed that solve the multi-dimensional and time-dependent linear and non-linear SchrÃ¶dinger and Helmholtz equations. We develop the mathematical tools that solve and simulate complex systems starting from first principles and realistic microscopic interactions. This often leads to large scale calculations on supercomputers.