The main thread in the research, running right back to my D.Phil, is the branching random walk. Recent applications of the theory to a number of problems in theoretical computer science, and connections with fractals and non-linear partial differential equations (pdes), have increased the profile of my work considerably. These avenues (theoretical computer science, fractal structures and non-linear pdes) continue to reveal fascinating and challenging problems.
The branching random walk forms part of the general area of branching processes. I have further papers on other aspects of branching processes; specifically, the collaborations with J. D'Souza, N.H. Bingham, O. Nerman and H. Cohn represent work on different areas under this heading.
In addition there is one series of papers (with C. Cannings) that deals with a problem in probability theory outside branching processes, a recent excursion into random walk theory, and another in large deviations and, with D. Penman, into random graphs.
For some years I had an interest in the statistical issues involved in combining and scaling examination marks. This falls within the psychometric tradition in statistics, and it is rather different from the probability theory that is my main interest. It turns out that examination marks provide an interesting example of the need for these techniques that throws up some new and interesting theoretical problems. I have supervised a successful research student (K.K. Yue)
in this area.
Finally, I have a few papers that are the result of providing statistical expertise to colleagues outside Mathematics. The most notable are a series of collaborations with T.R. Birkhead FRS.
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