Head of School and Professor of Applied Mathematics
We have a reputation for using sophisticated, rigorous mathematical techniques to solve real-world problems.
How would you summarise your research?
I enjoy using difficult, abstract mathematics to solve difficult and important real-world problems.
I enjoy using a combination of analytical and computational methods, the one informing the other. For example, accurate numerics can give guidance as to the topology and structure of solutions, for example singularities, which can then point the way to an analytic description. Equally asymptotic methods can be used in formulating, for example, far-field boundary condition, which can then be used to make numerical schemes more efficient.
What do you think makes the School distinctive?
The School places a lot of emphasis on intra- and inter-disciplinary research. We are well known for this type of research both across and outside the campus. We have a reputation for using sophisticated, rigorous mathematical techniques to solve real-world problems. Indeed, mathematics is benefitting from the need for numerous other disciplines (even non-science based areas) to become much more quantitative.
What do you enjoy most about teaching?
I enjoy showing how classical mathematics can be used to solve a number of modern-day problems. Taking financial mathematics as an example, there is no doubt that this has revolutionised many global financial markets, and is linked to the exchange of many billions of dollars of commercial trading on a daily basis.
How do you make your teaching up-to-date, innovative and inspirational?
I try to add topical items of news to motivate some of the mathematics used in my lectures.
What do you enjoy most about research?
I enjoy solving partial differential equations, both numerically and analytically. I also enjoy using techniques I have employed in one area (fluid dynamics) in another area (financial mathematics). Even though these may be regarded as completely disparate areas, nonetheless a lot of the mathematics is the same – this is the magic of mathematics!
What have been the highlights of your career?
Hosting several international conferences in Manchester. I have also been involved in the recruitment of a good number of staff, many of whom have become international leaders in their fields. Manchester is also now a major centre for financial mathematics, and I feel I have played a part in this.
When a student completes their course, what for you are the measures of success?
I like to think they have found some of the material studied challenging, interesting and useful.