Fellow and Tutor, University Lecturer in Mathematics, Professor of Combinatorics
I was an undergraduate in Edinburgh and then a research student and junior research fellow in Oxford. After that I had spells in London and in the USA, then returned here to Oxford in 1980, and I have been a Fellow of Corpus since 1989. Activities in Corpus over the years have included participation in various sports teams (still squash on occasion) and being Tutor for Graduates, Dean and Senior Tutor. I work both in the Mathematical Institute and in the Department of Statistics, and was Head of Department of the latter from 2005 to 2009. I am on the editorial boards of various journals, including Random Structures and Algorithms, and Combinatorics Probability and Computing.
Discrete mathematics, random structures, algorithms, combinatorial optimisation, mathematics of operational research. These topics are in the fertile and active area of mathematics that overlaps with theoretical computer science and the mathematics of operational research. The flavour could be described as pure mathematics inspired by applications.
In College, I usually cover pure mathematics and probability and statistics. In the University I teach various subjects in discrete mathematics and applied probability, and the mathematics of OR. It is a great pleasure to be able to stretch students individually, and to share the excitement of the penny dropping.
1 'Random channel assignment problems' We want to understand "typical" radio channel assignment problems. In one model, points corresponding to transmitters are thrown down at random in the plane, and we are to assign a radio channel to each point so that neighbouring points get different channels (to avoid interference). 'Random channel assignment in the plane', Random Structures and Algorithms 22 (2003) 187 - 212.
In a second model, each pair of transmitters u and v are given minimum distance 0,1 or 2 at random, and we are assign channels 1, 2, 3, .. so that the channels assigned to u and v must differ by at least the specified minimum distance (again, to avoid interference). 'On the span of random channel assignment problem', Combinatorica, 27 (2007) 183-203.
2 Load balancing - A simple but powerful method for minimising the maximum load of a processor involves picking two processor queues at random and joining the shorter.
'On the power of two choices': balls and bins in continuous time, Annals of Applied Probability 15 (2005) 1733-1764. (Joint with Malwina Luczak.)
'On the maximum queue length in the supermarket model, Annals of Probability 34 (2006) 493-527. (Joint with Malwina Luczak.)
3 Random planar graphs - There has been a huge and successful endeavour investigating random graphs where edges appear independently, but what if we wish to find typical properties of planar graphs, or some other structured class?
'Random planar graphs', J. Combinatorial Theory B 93 (2005) 187-206. (Joint with Angelika Steger and Dominic Welsh.) Random graphs on surfaces, J. Combinatorial Theory B 98 (2008) 778-797.