Dr Claire Gilson
Dr Gilson is a Senior Lecturer in the Department of Mathematics, University of Glasgow and was a Visiting Fellow on the Discrete Integrable Systems programme in 2009.
When did you become first interested in mathematics and what keeps your interest fresh?
I have been interested in mathematics as long back as I can remember. As a child I loved mathematical puzzles and finding things out about numbers. It's easy to keep a fresh interest as there are always new things to learn and discover.
Could you tell us a little about your career path so far and what your current research involves?
My first degree was in mathematics from Cambridge. I then moved to London and did my PhD in mathematical physics. I have to admit to not understanding mathematical physics very well. At the time many people were working on String theories, trying to obtain a mathematical theory which related to real particles. After my PhD I felt I wanted to do some more mathematics but in a more tangible area and got a job as a research assistant in Newcastle University working with Professor Neil Freeman on integrable systems and solitons. Solitons are particle like solutions to certain differential equations. After a couple of years I moved to a lectureship at Glasgow University and have been there ever since. I still work in the area of integrable systems. My main area has been in "direct methods" for generating exact solutions to these nonlinear equations. The work is mostly done with pen and paper and is a bit of a cross over between pure and applied mathematics, as I am interested in the structure of the equations, which have connections in algebra. I use the computer sometimes to help me with calculations and plot pictures of solutions. All my solutions are exact solutions without approximation, so I don't generally need the use of numerical routines.
What achievements are you most proud of?
I have two favourite bits of work. At the end of the 1980's 2-dimensional exponentially decaying lump solutions (called dromions) were discovered . These, for me, were very interesting and with a colleague, we set about looking at the asymptotic behaviour of these dromions. I recall staying up half the night for many nights doing and redoing these calculations until they were reduced to something moderately compact. We calculated the behaviour of these dromions before and after interactions with each other. The results were published in the Proceedings of the Royal Society . The other piece of work that I particularly like was much more recent and again with the same co-author. This is on solutions to the noncommutative KP equation . This was one of those pieces of work that started out quite awkward because of the noncommutative nature of the problem, but the more we worked on it the more we realized that the whole structure fitted together quite beautifully.
How do you achieve a balance between your work and homelife?
With difficulty! I now have 2 young children (6 and 7) so I tend not to work at the weekend. Quite often in term time when teaching I find myself going back to work at 10pm at night to prepare something for the morning because I haven't been able to get it done before 5pm when I need to leave to pick the children up.
What advice would you offer to young women who are just starting their careers in the mathematical sciences?
I think I would say just try to enjoy it. It's a great opportunity to meet interesting people and make a contribution to advancing science. It is difficult to manage your time especially when doing research as it takes up endless amounts of time to do, so if you enjoy it, stick with it, if you really don't enjoy it, find something else to do.
Has your visit to the Newton Institute been fruitful?
Yes, it has. It was a wonderful opportunity to work with some of the best people in the world in a relaxed and stimulating environment. I am still working on most the things that I started during my visit and the ideas generated will keep me busy for sometime to come.
References Boiti, M.; Leon, J. Jp.; Martina, L.; Pempinelli, F. Scattering of localized solitons in the plane. Phys. Lett. A 132 (1988), no. 8-9, 432--439.
 Gilson, C. R.; Nimmo, J. J. C. A direct method for dromion solutions of the Davey-Stewartson equations and their asymptotic properties. Proc. Roy. Soc. London Ser. A 435 (1991), no. 1894, 339--357.
 Gilson, C. R.; Nimmo, J. J. C. On a direct approach to quasideterminant solutions of a noncommutative KP equation. J. Phys. A 40 (2007), no. 14, 3839--3850.