Combinatorial Identities and their Applications in Statistical Mechanics

7 April to 11 April 2008

Isaac Newton Institute for Mathematical Sciences, Cambridge, UK

Dedicated to the memory of Pierre Leroux (1942 - 2008)

Organisers: Professor Abdelmalek Abdesselam (University of Virginia) and Professor Pierre Leroux (Université du Québec à Montréal)

in association with the Newton Institute programme Combinatorics and Statistical Mechanics (14 January to 4 July 2008)

Theme of Workshop:

The objective is to bring together combinatorialists, computer scientists, mathematical physicists and probabilists, to share their expertise regarding such combinatorial identities, with the hope of fostering progress in the area through cross-fertilization.

A preliminary list of topics of interest for the workshop is:

Identities related to classes of 1-2- or 3-connected graphs and their relations with the Mayer or viral expansion and the Legendre transform, applications of the dissymmetry theorem for trees, as well as variants of the exponential formulae with applications to the Potts model.

Forest and tree-sum identities in the theory of cluster and Mayer expansions in rigorous statistical mechanics and quantum field theory.

Graph invariants arising from Mayer and Ree-Hoover expansions.

Functional and differential equations for classes of combinatorial structures, for example maps, permutations, rooted trees, Feynman diagrams, related to physics.

Generalizations and applications of Kirchhoff's matrix-tree theorem, such as the parametric representation of Feynman diagrams in commutative and noncommutative quantum field theory, the Pfaffian-tree theorem, combinatorial applications of Grassmann-Berezin integration.

Keynote speakers will include:

Abdelmalek Abdesselam (UVa, Charlottesville), David Brydges (UBC, Vancouver), Roman Kotecky (Warwick and Prague), Christian Krattenthaler (Universität Wien), Gilbert Labelle (UQAM, Montréal), Gregor Masbaum (Jussieu), Aldo Procacci (UFMG, Belo Horizonte), Vincent Rivasseau (Paris-Sud), Alan Sokal (NYU and UCL), Andrea Sportiello (Milano), Alexander Varchenko (UNC, Chapel Hill), Xavier Viennot (Bordeaux).