My broad research interests lie in mathematics as applied to real world problems. Within this, my focus has been to understand biological processes, especially as related to diseases such as cancer and diabetes. The aim of my research is to build mathematical models based on in-vivo and in-vitro experiments with the aim of gaining some understanding and insight into phenomenon not well understood, such as drug resistance in cancer, or glucose metabolism in the case of diabetes mellitus. Working in conjunction with biologists is an emphasis here so that models developed are realistic.
In addition to the above research interests I have been working on mathematical problems in the application area of Finance. Most recently this has involved trying to model stochastic volatility. The entire option-pricing issue rests on good estimates of volatility. Volatility however is random and therefore to determine option prices that are close to market values one would like to be able to model volatility that is reflective of real world volatility, so that an options portfolio can be appropriately hedged.