The goal of this mini-course is to introduce the basic methods of enumerative combinatorics and the concepts of Statistical Mechanics which are at the hearth of the interactions between these two areas. The topics presented will include generating functions, combinatorial species, functional equations, asymptotics, classical models of statistical mechanics (polyominoes and animals, self-avoiding walks, gas models, Ising and Potts models, polymers and percolation), thermodynamic limits, phase transitions and Tutte polynomials.
The school is intended for graduate students, postdocs and researchers wishing to be introduced to these questions. It will be held in the Laurentians region, at the Far Hills Inn, located one hour north of Montreal in Val-Morin, Quebec.
Centre de recherches mathématiques
Scientific organizers: M. Bousquet-Mélou (Bordeaux), P. Leroux (UQAM), T. Guttmann (Melbourne) and A. Sokal (New York)
This workshop will include expository talks as well as presentations on current research on combinatorial problems raised by statistical mechanics. Topics of interest include: enumerative problems related to the classical models of statistical mechanics, algebraic methods related to functional equations, Mayer's theory and graph weights, Potts model on graphs, planar maps and 2-dimensional quantum gravity, Feynman diagrams, etc.
The meeting will be held at the CRM.