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This conference is a celebration of Prof. Tony Guttmann’s 70th birthday, an acknowledgment of his enormous contribution to Mathematics in Australia and of his field of research: Critical Phenomena in Statistical Mechanics. Amongst Prof. Guttmann many contributions to Australian Mathematics was his initial contribution to the founding of ½ñÈÕ³Ô¹Ï. Attending this conference are several international and national leaders in the field of Critical Phenomena, Enumerative Combinatorics, Algebraic Combinatorics and Computational Algorithms. These are fields of mathematics that all play a signification part in the mathematical understanding of Critical Phenomena.