Career timeline
- 2016-present Professor of Applied Mathematics, School of Mathematics, University of Manchester
- 2014-present EPSRC Research Fellow, project NEMESIS, School of Mathematics, University of Manchester
- 2012-2016 Reader in Applied Mathematics, School of Mathematics, University of Manchester
- 2011-2012 Senior Lecturer in Applied Mathematics, School of Mathematics, University of Manchester
- 2009-2011 Lecturer in Applied Mathematics, School of Mathematics, University of Manchester
- 2007-2009 Faculty Research Fellow, School of Mathematics, University of Manchester
- 2004-2007 EPSRC Postdoctoral Research Fellow, School of Mathematics, University of Manchester
- 2001-2004 PhD in Applied Mathematics, School of Mathematics, University of Manchester. Supervised by Prof. I. D. Abrahams and with sponsorship from Thales Underwater Systems
- 1999-2000 MSc in Mathematical Modelling and Scientific Computing (Distinction), Oxford Centre for Industrial and Applied Mathematics, University of Oxford, supervised by Dr D. J. Allwright.
- 1996–1999 BSc in Mathematics (First Class Honours), Department of Mathematics, University of Bristol.
If anyone is interested - here is a quick bio:
In 1996 I went to Bristol to study Maths. This was a revelation! Analysis, number theory and the realization that you could carefully model the motion of fluids with mathematics. For the first two years I studied a broad range of topics, not really wishing to choose between Applied and Pure mathematics options. In third year however, I decided that Applied Mathematics was for me and I targeted Methods courses, Complex Analysis, Fluids, Modelling and anything that was in any way Applied. I was lucky enough to be taught by some excellent people - Andrew Hogg, Rich Kerswell and David Evans, all superb applied mathematicians and fluid dynamicists. I was also taught by the brilliant and eccentric Phillip Drazin and Howell Peregrine who sadly have now passed on. In my third year I studied for a project with Andy Woods in two-phase slow flows on inclined (porous) planes. Most of this involved firstly trying to understand Andy's papers and I then tried to extend the work in various directions (usually in rather naive ways, but that is the nature of an undergraduate project!). I was also lucky enough to be surrounded by very interested students, who asked interesting questions and made me think hard. Towards the end of my third year I realized that applied maths and modelling was for me and I decided that I was really interested in the modelling route and so I went to OCIAM at Oxford to study for the MSc there in Mathematical Modelling and Scientific Computing.
The MSc at Oxford was very intense. Right from the start. This was mainly due to the short terms I guess, but also there were many contact hours and the modelling classes alone took up a significant amount of time, since one had to meet up outside class time to get stuff done. However all of this was excellent training, again for making one think hard! For the first two semesters I was supervised by John Ockendon in OCIAM, who was (and still is) very supportive of my interests in applied mathematics. When it came to choosing a dissertation I looked for a project with industry and the project entitled "Elastic wave scattering from a strained region", sponsored by the then "Thomson Marconi Sonar" (now Thales Underwater Systems), caught my attention. Little did I know it at the time but this choice was to be very influential in my career. David Allwright supervised me on this project. David is an amazing mathematician and it was a pleasure to be supervised by him. I had no background in solid mechanics and so I had a lot of catching up to do but his encouragement and guidance ensured that I ended up delivering a dissertation that I was very happy with. It did not really answer too many questions but it posed many! And it got me thinking about this and related problems in further detail. I was also taught by some superb people at Oxford - Jon Chapman, Andrew Fowler, Endre Suli, Nick Trefethen, to name but a few.
I needed a break from study and so, after being offered a PhD with David Abrahams in the Mathematics Department at Manchester, I deferred this position by a year and travelled around the world with my (now wife) Debbie. This was the best thing I ever did. We had no money but no responsibilities, being blessed with only a little student debt - how different things were then. And so we went to Manchester in the summer of 2001 fully reinvigorated to start afresh. David wanted me to look at some problems in homogenization. He was just becoming interested in the topic, having seen a lot of people use the methods in a variety of ways. Early in 2002, Thomson Marconi (who are based in Cheadle in fact) expressed an interest to carry on working on some problems associated with my thesis, especially since we were now working on homogenization - they had worked with David in the past and so this was all very fortuitous. After doing some work on Matrix Wiener-Hopf, trying to prove that the method they were using for multiple scattering from an inhomogeneous half-space had some validity, we decided that we needed to understand all of the work in much more detail. So we backtracked. We did some work on asymptotic homogenization, showing that a fully dynamic formulation is a much better way to do things than the usual classic, statics approach. In particular we used a multiple scales approach with a stretched scaling - very few people use this approach but it is very elegant and necessary if you want to get higher order terms correct. We then showed that the method that Thales were using to predict their effective properties ignored multiple interaction and so was only valid at small volume fraction - an important result. However we used the starting point for their method, the integral equations of linear elasticity, to develop a new integral equation approach to homogenization. We like this method because you can derive analytical expressions for effective properties that have a nice, clean form in terms of the various parameters of the problem. We are still trying to get this method working in three dimensions though - this is the holy grail! During the PhD I became very interested in the link between homogenization and multiple scattering. In the low frequency limit, generally one should recover the homogenized limit and so there is a direct link. At the time also, a number of people were getting interested in multiple scattering again, looking at the Foldy, Waterman-Truell and Lloyd Berry results once again.
David was an excellent supervisor (and is a fantastic mathematician, although since he is now a close colleague he will blush at that!), he guided the PhD but allowed me freedom to develop my own interests. As such I became interested in thermoelasticity and also nonlinear elastic pre-stress, which I rediscovered, having studied it in my MSc dissertation. I also attended a number of very interesting conferences which allowed me to see the breadth of applied mathematics. Once again I was surrounded by good people. My office-mates were Ian Thompson (now a lecturer at Liverpool) and Ben Veitch (now a research scientist working for Schlumberger in Cambridge) and I also studied at the same time as Anthony Thornton (now at Twente, in the Netherlands). Discussing mathematics and its applications with these three was a real joy and this made the PhD all the more enjoyable. I was also fortunate enough to have great support at that time within the Maths department at Manchester, namely from people like Matthias Heil, Andrew Hazel, Anne Juel, Rich Hewitt and Nico Gray. I applied for an EPSRC Postdoctoral Fellowship in 2003 and was successful, beginning the position (in Manchester) after I finished my PhD in Sept 2004. Ben, Anthony and Ian are pictured on the right here - we had a chance meeting in Manchester recently which was very pleasant!
The fellowship was very influential on my career. It allowed me the freedom to travel a lot, meet lots of people and talk with them about applied mathematics and science. I learnt a great deal and made a lot of collaborations, many of which I still keep today. Strangely, I did not publish that much during this period. This was almost certainly because I was working on so many different projects and with numerous people. This could have been catastrophic of course had nothing come of any of it but in time things did work out, although I would not advise someone these days to do the same as this - publish or perish is more pertinent than ever now of course. Manchester offered me a follow-on faculty fellowship in 2007 which blended into a lecturership position in 2009. And I have been here ever since.
Since my appointment David and I have developed things significantly. Together, we established the WICC waves group in 2010 and have developed links with Thales and other industrial collaborators (most recently Dyson) significantly. We have since supervised (and currently supervise) a large number of PhD students, working on a broad range of topics. And the group continues to grow. In 2016 David took up the prestigious position of Director of the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge. David remains a member of WICC of course currently spending most Fridays in Manchester with the group.
The department at Manchester (now School) has changed enormously since I came here in 2001. The merger in 2004 and massive investment and growth of the University have had a big impact in all areas. The School goes from strength to strength and it is nice to see Applied Mathematics at Manchester now being seen as very broad, not "just" based on its incredible history of fluids, even though that history is rather distinguished. Industrial Mathematics (in its broadest terms) is growing steadily which gives rise to a number of opportunities, not only in high quality, publishable and applicable research, but also in terms of employability and opportunities for students.
In 1996 I went to Bristol to study Maths. This was a revelation! Analysis, number theory and the realization that you could carefully model the motion of fluids with mathematics. For the first two years I studied a broad range of topics, not really wishing to choose between Applied and Pure mathematics options. In third year however, I decided that Applied Mathematics was for me and I targeted Methods courses, Complex Analysis, Fluids, Modelling and anything that was in any way Applied. I was lucky enough to be taught by some excellent people - Andrew Hogg, Rich Kerswell and David Evans, all superb applied mathematicians and fluid dynamicists. I was also taught by the brilliant and eccentric Phillip Drazin and Howell Peregrine who sadly have now passed on. In my third year I studied for a project with Andy Woods in two-phase slow flows on inclined (porous) planes. Most of this involved firstly trying to understand Andy's papers and I then tried to extend the work in various directions (usually in rather naive ways, but that is the nature of an undergraduate project!). I was also lucky enough to be surrounded by very interested students, who asked interesting questions and made me think hard. Towards the end of my third year I realized that applied maths and modelling was for me and I decided that I was really interested in the modelling route and so I went to OCIAM at Oxford to study for the MSc there in Mathematical Modelling and Scientific Computing.
The MSc at Oxford was very intense. Right from the start. This was mainly due to the short terms I guess, but also there were many contact hours and the modelling classes alone took up a significant amount of time, since one had to meet up outside class time to get stuff done. However all of this was excellent training, again for making one think hard! For the first two semesters I was supervised by John Ockendon in OCIAM, who was (and still is) very supportive of my interests in applied mathematics. When it came to choosing a dissertation I looked for a project with industry and the project entitled "Elastic wave scattering from a strained region", sponsored by the then "Thomson Marconi Sonar" (now Thales Underwater Systems), caught my attention. Little did I know it at the time but this choice was to be very influential in my career. David Allwright supervised me on this project. David is an amazing mathematician and it was a pleasure to be supervised by him. I had no background in solid mechanics and so I had a lot of catching up to do but his encouragement and guidance ensured that I ended up delivering a dissertation that I was very happy with. It did not really answer too many questions but it posed many! And it got me thinking about this and related problems in further detail. I was also taught by some superb people at Oxford - Jon Chapman, Andrew Fowler, Endre Suli, Nick Trefethen, to name but a few.
I needed a break from study and so, after being offered a PhD with David Abrahams in the Mathematics Department at Manchester, I deferred this position by a year and travelled around the world with my (now wife) Debbie. This was the best thing I ever did. We had no money but no responsibilities, being blessed with only a little student debt - how different things were then. And so we went to Manchester in the summer of 2001 fully reinvigorated to start afresh. David wanted me to look at some problems in homogenization. He was just becoming interested in the topic, having seen a lot of people use the methods in a variety of ways. Early in 2002, Thomson Marconi (who are based in Cheadle in fact) expressed an interest to carry on working on some problems associated with my thesis, especially since we were now working on homogenization - they had worked with David in the past and so this was all very fortuitous. After doing some work on Matrix Wiener-Hopf, trying to prove that the method they were using for multiple scattering from an inhomogeneous half-space had some validity, we decided that we needed to understand all of the work in much more detail. So we backtracked. We did some work on asymptotic homogenization, showing that a fully dynamic formulation is a much better way to do things than the usual classic, statics approach. In particular we used a multiple scales approach with a stretched scaling - very few people use this approach but it is very elegant and necessary if you want to get higher order terms correct. We then showed that the method that Thales were using to predict their effective properties ignored multiple interaction and so was only valid at small volume fraction - an important result. However we used the starting point for their method, the integral equations of linear elasticity, to develop a new integral equation approach to homogenization. We like this method because you can derive analytical expressions for effective properties that have a nice, clean form in terms of the various parameters of the problem. We are still trying to get this method working in three dimensions though - this is the holy grail! During the PhD I became very interested in the link between homogenization and multiple scattering. In the low frequency limit, generally one should recover the homogenized limit and so there is a direct link. At the time also, a number of people were getting interested in multiple scattering again, looking at the Foldy, Waterman-Truell and Lloyd Berry results once again.
David was an excellent supervisor (and is a fantastic mathematician, although since he is now a close colleague he will blush at that!), he guided the PhD but allowed me freedom to develop my own interests. As such I became interested in thermoelasticity and also nonlinear elastic pre-stress, which I rediscovered, having studied it in my MSc dissertation. I also attended a number of very interesting conferences which allowed me to see the breadth of applied mathematics. Once again I was surrounded by good people. My office-mates were Ian Thompson (now a lecturer at Liverpool) and Ben Veitch (now a research scientist working for Schlumberger in Cambridge) and I also studied at the same time as Anthony Thornton (now at Twente, in the Netherlands). Discussing mathematics and its applications with these three was a real joy and this made the PhD all the more enjoyable. I was also fortunate enough to have great support at that time within the Maths department at Manchester, namely from people like Matthias Heil, Andrew Hazel, Anne Juel, Rich Hewitt and Nico Gray. I applied for an EPSRC Postdoctoral Fellowship in 2003 and was successful, beginning the position (in Manchester) after I finished my PhD in Sept 2004. Ben, Anthony and Ian are pictured on the right here - we had a chance meeting in Manchester recently which was very pleasant!
The fellowship was very influential on my career. It allowed me the freedom to travel a lot, meet lots of people and talk with them about applied mathematics and science. I learnt a great deal and made a lot of collaborations, many of which I still keep today. Strangely, I did not publish that much during this period. This was almost certainly because I was working on so many different projects and with numerous people. This could have been catastrophic of course had nothing come of any of it but in time things did work out, although I would not advise someone these days to do the same as this - publish or perish is more pertinent than ever now of course. Manchester offered me a follow-on faculty fellowship in 2007 which blended into a lecturership position in 2009. And I have been here ever since.
Since my appointment David and I have developed things significantly. Together, we established the WICC waves group in 2010 and have developed links with Thales and other industrial collaborators (most recently Dyson) significantly. We have since supervised (and currently supervise) a large number of PhD students, working on a broad range of topics. And the group continues to grow. In 2016 David took up the prestigious position of Director of the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge. David remains a member of WICC of course currently spending most Fridays in Manchester with the group.
The department at Manchester (now School) has changed enormously since I came here in 2001. The merger in 2004 and massive investment and growth of the University have had a big impact in all areas. The School goes from strength to strength and it is nice to see Applied Mathematics at Manchester now being seen as very broad, not "just" based on its incredible history of fluids, even though that history is rather distinguished. Industrial Mathematics (in its broadest terms) is growing steadily which gives rise to a number of opportunities, not only in high quality, publishable and applicable research, but also in terms of employability and opportunities for students.