Combinatorial identities and their applications in statistical mechanics

Workshop theme

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).

Applications for this workshop are now closed

Timetable

Monday 7th April 2008
09:00 to 09:55	Registration	No Room Required
10:00 to 11:11	Gilbert Labelle UQAM - Université du Québec à Montréal Introduction to species and combinatorial equations	Room 1
11:11 to 11:30	Coffee	No Room Required
11:30 to 12:30	Alan Sokal An introduction to the Mayer expansion	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 15:00	Xavier Gérard Viennot Université Bordeaux 1 Introduction to the theory of heaps of pieces with applications to statistical mechanics and quantum gravity	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Roman Kotecky University of Warwick Cluster expansions (a historical overview)	Room 1
16:30 to 17:15	Marc Noy Universitat Politècnica de Catalunya Graph classes with given 3-connected components: asymptotic counting and critical phenomena	Room 1
17:15 to 17:30	Poster Presentation	No Room Required
17:30 to 18:30	Welcome Wine Reception	No Room Required
18:45 to 19:30	Dinner at Wolfson Court	No Room Required

Tuesday 8th April 2008
09:00 to 10:00	Aldo Procacci Universidade Federal de Minas Gerais (UFMG) Improved bounds on cluster expansion of the abstract polymer model (via the Penrose identity)	Room 1
10:00 to 11:00	David Chandos Brydges University of British Columbia Counting with Gaussian integrals and cluster expansions	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:30	Abdelmalek Abdesselam University of Virginia Field theoretic cluster expansions and the Brydges-Kennedy forest sum formula	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 15:00	Alexander Varchenko University of North Carolina Determinant formulas for pairing matrices of arrangements of hyperplanes	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:15	Olivier Bernardi A bijection between subgraphs and orientations based on the combinatorics of the Tutte polynomial	Room 1
16:15 to 17:15	Gilbert Labelle UQAM - Université du Québec à Montréal Mayer polytopes and divided differences	Room 1
18:45 to 19:30	Dinner at Wolfson Court	No Room Required

Wednesday 9th April 2008
09:30 to 10:15	Roberto Fernandez Université de Rouen Analyticity of the pressure of the hard-sphere gas	Room 1
10:15 to 11:00	Milos Zahradnik Charles University, Prague Integral equations for cluster expansion sums of polymer models with (soft) repulsion	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:30	Vincent Rivasseau Université Paris Saclay Introduction to non commutative field theory	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 15:00	Andrea Sportiello Università degli Studi di Milano Potts model, O(n) non-linear sigma-models and spanning forests	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:15	Seth Chaiken University at Albany, State University of New York An extensor tree theorem and a Tutte identity for graphs with distinguished port edges	Room 1
16:15 to 17:00	Razvan Gurau Université Paris Saclay Parametric representation of non commutative quantum field theory	Room 1
18:45 to 19:30	Dinner at Wolfson Court	No Room Required

Thursday 10th April 2008
09:30 to 10:15	Martin Loebl Charles University, Prague Enumeration of planar graphs by matrix integrals	Room 1
10:15 to 11:00	Joanna Ellis-Monaghan Saint Michael's College, Vermont Multivariable Tutte and transition polynomials	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:30	Gregor Masbaum Institut de Mathématiques de Jussieu Alexander-Conway polynomial, milnor numbers, and the Pfaffian matrix-tree theorem	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
15:00 to 15:30	Tea	No Room Required
15:30 to 16:15	Kurusch Ebrahimi-Fard Université de Haute-Alsace Solving Bogoliubov's recursion in renormalisation using a simple algebraic identity	Room 1
16:15 to 17:00	Adrian Tanasa Max-Planck-Institut für Mathematik, Bonn Connes-Kreimer Hopf algabra for non-commutative field theory	Room 1
17:00 to 17:45	Mihai Ciucu Indiana University Combinatorial identities and the correlation function gaps in dimer packings	Room 1
19:30 to 23:00	Conference Dinner at Christ's College (The Dining Hall)	No Room Required

Friday 11th April 2008
09:30 to 10:15	Forest-root formulas in statistical physics	Room 1
10:15 to 11:00	Jacques Magnen Centre de Physique Théorique de l’Ecole Polytechnique (CPHT) Constructive field theory without tears	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:30	Christian Krattenthaler Technische Universität Wien Identities for fully packed loop configurations and semistandard tableaux	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:15 to 15:00	Thomas Prellberg Queen Mary University of London Counting partially directed walks in a symmetric wedge	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:15	Cyril Banderier Université Paris 13 Enumeration and asymptotics of random walks and maps	Room 1
16:15 to 17:00	William Faris University of Arizona A rosetta stone: combinatorics, physics, probability	Room 1
18:45 to 19:30	Dinner at Wolfson Court	No Room Required

Speakers

Abdelmalek Abdesselam University of Virginia
Cyril Banderier Université Paris 13
Olivier Bernardi
David Chandos Brydges University of British Columbia
Seth Chaiken University at Albany, State University of New York
Mihai Ciucu Indiana University
Kurusch Ebrahimi-Fard Université de Haute-Alsace
Joanna Ellis-Monaghan Saint Michael's College, Vermont
William Faris University of Arizona
Roberto Fernandez Université de Rouen
Razvan Gurau Université Paris Saclay
Roman Kotecky University of Warwick
Christian Krattenthaler Technische Universität Wien
Gilbert Labelle UQAM - Université du Québec à Montréal
Martin Loebl Charles University, Prague
Jacques Magnen Centre de Physique Théorique de l’Ecole Polytechnique (CPHT)
Gregor Masbaum Institut de Mathématiques de Jussieu
Marc Noy Universitat Politècnica de Catalunya
Thomas Prellberg Queen Mary University of London
Aldo Procacci Universidade Federal de Minas Gerais (UFMG)
Vincent Rivasseau Université Paris Saclay
Alan Sokal
Andrea Sportiello Università degli Studi di Milano
Adrian Tanasa Max-Planck-Institut für Mathematik, Bonn
Alexander Varchenko University of North Carolina
Xavier Gérard Viennot Université Bordeaux 1
Milos Zahradnik Charles University, Prague

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