Keynote Speakers
Prof.
Peter Cameron
University of St Andrews
Peter Cameron is professor of Mathematics at the University of St Andrews, and professor emeritus at Queen Mary University of London, having previously held a position at Oxford University. He was awarded both the Junior and Senior Whitehead Prizes of the London Mathematical Society and the Euler Medal of the Institute of Combinatorics and its Applications. He has worked in various parts of combinatorics, group theory, logic and statistics, and has written more than 350 papers with over 200 coauthors (including Paul Erdős). He has recently been involved with a large project with mainly Indian mathematicians studying graphs defined on groups.
Speech Title: "The ADE Affair"
Abstract: The Coxeter–Dynkin diagrams of type ADE (shown above) are almost ubiquitous in mathematics, arising in areas from Lie algebras to general relativity, representation theory to finite graph theory, regular polyhedra to singularity theory. In 1978, Vladimir Arnold proposed the problem of explaining their extremely wide range as a “moden Hilbert problem”. This problem is by no means solved, and recent developments have added more occurrences such as cluster algebras. In my talk I will explain some of the many occurrences of these diagrams, and some of the connections between them. A highlight is the observation of John McKay (the person who originated “monstrous moonshine”) on a direct connection between quivers for the binary polyhedral groups and the ADE root systems. It must be said, though, that there is much still to do!
Prof.
R. A. Bailey
University of St Andrews
R. A. Bailey is Professor of Statistics at the University of St Andrews, and a Fellow of the Royal Society of Edinburgh. She worked for the Medical Research Council's Air Pollution Research Unit before studying at the University of Oxford, where she obtained a BA in Mathematics and a DPhil in Group Theory. As a post-doctoral fellow at the University of Edinburgh she learnt how to apply group theory to problems in design of experiments. She spent ten years applying this knowledge in the Statistics Department at Rothamsted Experimental Station, before moving to academia, being Head of Department or School at Goldsmiths College and at Queen Mary College, both in the University of London. She was President of the then-British Region of the International Biometric Society from 2000 to 2002, and has also served on various committees of the London Mathematical Society, the Royal Statistical Society and the Institute of Mathematical Statistics.
Speech Title: "Designs on Strongly-regular Graphs"
Abstract: Some particularly nice graphs are the strongly-regular graphs. Their edges and non-edges form the associate classes of an association scheme. The corresponding Bose–Mesner algebra (linear combinations of the adjacency matrices) has three common eigenspaces, one of which is V0, which consists of the constant vectors. In classical work on design of experiments, the experimental units are grouped into b blocks of size k. This corresponds to the strongly-regular graph consisting of b complete graphs of size k, with no edges between them. In some other experiments, the experimental units are all pairs of individuals who have to undertake a given task together. If all such pairs are used exactly once each, then the set of pairs forms a triangular association scheme. Two types of design are particularly important. In balanced designs, the variance of the estimated difference between any two treatments is the same. In orthogonal designs, the linear combination of responses which gives the best unbiased estimator of any difference between treatments is obtained by simple averaging. Such designs are often said to have commutative orthogonal block structure. I will give some constructions for balanced designs and some for designs which have commutative orthogonal block structure, in each scenario.