My research interests are broad. They include theoretical fluid mechanics, reaction-diffusion phenomena,spectral analysis and computation, the algebraic structure and simulation of stochastic differential systems, non-commutative integrable systems and coagulation phenomena.

After finishing my PhD at Imperial in 1993, I spend three years at the University of Arizona. Then two years at Nottingham and two years at Imperial as a temporary lecturer followed. I joined Heriot-Watt in September 2000.

Director of Postgraduate Research

In the world of AI proofs in mathematics it is important to remind ourselves of some answers to the following question.

What are mathematicians good for, and why are we valuable to society? 

My perpective on this is as follows. As mathematicians we qualify and quantify natural processes. These could be in the fields of physics, chemistry, finance, biology and so forth. We try to write down a model for the natural process concerned. Invariably such a model will only be approximate of course, but we ca still use it to our advantage depending on the error we are willing to accept or tolerate. What do we do with that model? We make predictions which might be helpful to the public. For example weather predictions are exteremly helpful, or predicting climate change evolution is obviosuly very important. We also provide optimal solutions to scenarios, for example how to get from A to B using the least amount of energy or time. Optimisation is an integral part of LLMs, for another example. However, we can take this further. We can use our models to control systems, for example, the weather, though maybe a better example is the following. An epidemiological model might predict the future outcome of a disease epidmic like COVID 19. However we can put in controls, such as social distancing, or immunisation programmes, and see from the model what the outcomes will be. We can then vary the intensity or types of controls to try to obtain the optimal outcome. 

AI can do a lot of these tasks. At the moment at least, we're still the ones asking the questions, but for how long? Of course, someone needs to understand what's going on, and that's another role mathematicians can fulfill.