Dominic Welsh is a leading contributor to combinatorial mathematics in several ways. In research, his significant contributions began with his doctoral thesis, "On stochastic processes, with special reference to percolation theory". This was a basis for much further work, including the Russo-Seymour-Welsh theorem.
Professor Jim Geelen is already a world leader in the areas of combinatorial optimization and matroid theory. The referees describe him as an "outstanding talent" and a "very creative and original researcher" with a "huge international reputation".
As a graduate student of Professor Christopher Godsil, University of Waterloo, Michael Newman wrote an outstanding dissertation which presents extensions and applications of the Delsarte-Hoffman bound on the size of independent sets in graphs. The thesis interweaves the solutions of three intriguing yet ostensibly unrelated problems into a unified tapestry by virtue of their common methodological treatment. The results obtained are important and the exposition first-rate.
Professor Penny E. Haxell works in combinatorics and graph theory, focussing on combinatorial, probabilistic and, more recently, topological tools in a very fascinating manner. In all her work she exhibits impressive capability, originality and technical ability, and her pioneering work is well known internationally.
Her work in 1995 with Kohayakawa and Luczak, led to a profound study of Szemeredi's lemma in a sparse setting, and their methods are still being developed fruitfully by others.