Phillip L. Wilson
Department of Mathematics and Statistics
Room 702, Erskine Building
Want to do a PhD, MSc, Honours, or Summer project with me? Great! Read below to see the sorts of things I am interested in, have a look at the preprints available from the navi at left, and then email me (address above), and we'll see what we can do.
I used to begin this section with that I thought was a clever byline: "Real world inspiration to discover interesting mathematics". While I still aspire to this being true, I'm not sure that it ever has been for me. I strongly feel that the mathematisation of biology, which is proceeding apace, will lead to quite novel forms of mathematics; I can't express this better than JE Cohen does here. This opinion has been slightly modified recently by reading some work (by Kauffman, Pilkey, and others) which reminds me that math is one thing and the real world quite another. However, to date, the closest I have come to "discovering" new mathematics is "discovering" mathematics which is new to me.
There is a related sense in which I have been discovering something, however: when old math is applied to new problems, real discovery is taking place. Insight is gained. And this is a two-way process: most importantly, we gain insight into the phenomenon under investigation. But we also gain some insight into the mathematics: every new sum whose solution is "2" is a new fact about the number 2.
But anyway, I do not claim to know what the "real world" is, nor whether mathematics is "discovered". To me, mathematics and the thinking life in general is about having fun, being transformed by the process, and sharing with and encouraging others. I'm fascinated by this beautiful world of ours, internal and external, and I want to have fun discovering, discussing, disseminating, and dreaming about it.
However, if you insist, the general areas in which I work are theoretical fluid dynamics and mathematical modelling in biology and industry. Specific inspirations include how blood flows in the brain, how biological membranes get their properties, how objects embedded in those membranes influence disease, the origins of visual aura and cortical spreading depression, how lung tumours move and can be better treated, how falling granular bodies interact with one another, how air flows through pipes, the role of narrative in eduction, why applied mathematics is even possible, and more besides. Rather than me summarising my work here, I recommend that you follow Stephen Jay Gould's advice and return to the original sources: read my outputs available from the navi at left. (Since some projects are nascent and are yet to produce outputs, please feel free to contact me to learn more.)
I have occasionally attempted to explain the fun and excitement of mathematics to a general audience. I love doing so in the flesh and would be happy to come and talk to your school. I also write for the public, and most of this work is freely available on the web. Go to the "Official" Research Profile in the navi at top left. The pop science writing is listed as "Other" under "Publications".
Latest update: 20130614.