Combinatorics and statistical mechanics

Programme theme

The past half-decade has seen an increasing interaction between combinatorialists, probabilists, computer scientists and theoretical physicists concerned broadly with the study of "probability theory on graphs" or "statistical mechanics on graphs".

The programme will build on this cross-fertilisation. It is particularly timely for a number of reasons:

methods from mathematical physics are beginning to make their mark on previously intractable combinatorial problems;
increasing computer power, together with the wide availability of symbolic-algebra packages,
has brought the possibility of exploration of non-trivial examples;
phase transitions are increasingly being investigated on a wide variety of combinatorial structures, including matroids, set partitions and constraint satisfaction problems, as well as graphs.

In this interdisciplinary field, the questions being investigated typically arise naturally in combinatorics or probability, but key elements of the intuition needed for their solution often come from physics, for example from the theory of phase transitions and critical phenomena.

Particular topics to be addressed by the programme and its workshops will include: zeros of combinatorial polynomials, including the chromatic, flow, reliability and Tutte polynomials; Markov-chain Monte Carlo methods; combinatorial identities and their applications in statistical mechanics; use of methods from statistical mechanics and quantum field theory in combinatorial enumeration; correlation inequalities; and phase transitions in combinatorial structures.

Support from the National Science Foundation

Limited travel and subsistence funds are available from an NSF grant to support the participation of researchers (of any nationality) affiliated to a U.S. institution. The aim is to facilitate the participation of those who may not have access to alternative funding sources for their travel and subsistence, particularly young researchers, women, minorities, and researchers based at small colleges.

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Applicants for support should include a brief letter indicating their mathematical interests and reasons for wishing to participate in the programme, their first and second choices for dates of stay, and their other funding sources (if any). They should also send a CV and, in the case of graduate students, a letter of recommendation from the dissertation advisor.

Click here to download the programme's final scientific report

Preprints

Title	Year	Programme
Weighted enumeration of spanning subgraphs with degree constraints Authors: David Wagner Download PDF	2007	CSM	21 October 2016
A combinatorial proof of Rayleigh monotonicity for graphs Authors: J Hladky, MA Lacroix, David Wagner, J Cibulka Download PDF	2007	CSM	21 October 2016
Zero-free regions for multivariate Tutte polynomials (alias Potts-model partition functions) of graphs and models Authors: Bill Jackson, Alan Sokal Download PDF	2007	CSM	21 October 2016
Enumeration of the degree sequences of non-separable graphs and connected graphs Authors: OJ Rodseth, James Sellers, H Tverberg Download PDF	2007	CSM	21 October 2016
Quantum spaces associated to multipermutation solutions of level 2 Authors: Tatiana Gateva-Ivanova, S Majid Download PDF	2007	CSM	21 October 2016
Counting 2-connected deletion-minors of binary matroids Authors: Bill Jackson Download PDF	2007	CSM	21 October 2016
Counting defective parking functions Authors: Daniel Johannsen, Thomas Prellberg, Pascal Schweitzer, Peter Cameron Download PDF	2007	CSM	21 October 2016
Oligomorphic permutation groups Authors: Peter Cameron Download PDF	2007	CSM	21 October 2016
Sparse random graphs with clustering Authors: Svante Janson, O Riordan, Bela Bollobas Download PDF	2007	CSM	21 October 2016
The exact evaluation of the corner-to-corner resistance of an $M ×N$ resistor network: asymptotic expansion Authors: FY Wu, JW Essam Download PDF	2007	CSM	21 October 2016
Transforms and minors for binary functions Authors: Graham Ernest Farr Download PDF	2007	CSM	21 October 2016
Computing Tutte polynomials Authors: David J Pearce, Gordon Royle, Gary Haggard Download PDF	2007	CSM	21 October 2016

Workshops

CSMW06

Seminars

Thursday 31st January 2008
14:00 to 15:00	David Wagner University of Waterloo Generalisations of the Heilmann-Lieb theorem, with proofs	Room 2

Thursday 7th February 2008
11:00 to 12:30	David Jackson University of Waterloo An inequality for Tutte polynomials	Room 1

Thursday 14th February 2008
11:30 to 12:30	Peter Cameron Queen Mary University of London Orbital chromatic and flow polynomials	Room 2
16:00 to 17:00	Graham Ernest Farr Monash University Generalised Tutte polynomials	Room 2

Tuesday 19th February 2008
11:15 to 13:00	Peter Cameron Queen Mary University of London The carpark problem	Discussion Room

Wednesday 20th February 2008
15:00 to 17:00	Mark Jerrum Queen Mary University of London Mixing 101	Room 2

Thursday 21st February 2008
16:00 to 17:00	Abstract polymers with general pair interactions	Room 2

Monday 25th February 2008
11:00 to 12:00	James Sellers Pennsylvania State University Graphical partitions	Discussion Room

Tuesday 26th February 2008
11:00 to 12:00	Graph polynomials from an algebraic point of view	Discussion Room

Tuesday 4th March 2008
11:00 to 12:00	Peter Cameron Queen Mary University of London Graph polynomials from an algebraic point of view	Discussion Room

Thursday 6th March 2008
11:30 to 12:30	Roger Emil Behrend Cardiff University Osculating paths and oscillating tableaux	Room 2
16:00 to 17:00	Aldo Procacci Universidade Federal de Minas Gerais (UFMG) The Blume-Emery-Griffiths model with infinite range interactions in the low temperature disordered phase	Room 2

Tuesday 11th March 2008
11:00 to 13:00	Peter Cameron Queen Mary University of London Algebraic aspects of chromatic roots	Discussion Room

Wednesday 12th March 2008
15:15 to 16:00	David Wagner University of Waterloo Connections between combinatorics and statistical mechanics	Room 1

Thursday 13th March 2008
11:30 to 12:30	Alan Sokal Complete monotonicity for inverse powers of some combinatorially defined polynomials	Discussion Room

Tuesday 18th March 2008
14:00 to 15:00	Simone Severini University of Waterloo Combinatorics and quantum information theory	Room 1
15:00 to 16:00	Peter Cameron Queen Mary University of London Algebraic aspects of chromatic roots	Room 2

Wednesday 19th March 2008
15:00 to 16:00	Senya Shlosman Centre de Physique Théorique, Marseille Gibbs ensembles of nonintersecting paths, and determinantal processes	Room 1

Thursday 20th March 2008
11:00 to 12:00	Tatiana Gateva-Ivanova Bulgarian Academy of Sciences Set-theoretic solutions of the Yang-Baxter equation - a combinatorial approach	Room 1
15:00 to 17:00	Mark Jerrum Queen Mary University of London Mixing 101	Room 2

Wednesday 2nd April 2008
14:00 to 15:00	James Sellers Pennsylvania State University Enumeration of the degree sequences of non-separable graphs and connected graphs	Room 2

Wednesday 16th April 2008
15:00 to 16:00	Gordon Royle University of Western Australia Matroids with nine elements	Room 1

Thursday 17th April 2008
11:00 to 12:00	Martin Loebl Charles University, Prague Some notes on the combinatorial zeta function	Room 1
14:00 to 15:30	CSM informal talks	Discussion Room

Wednesday 30th April 2008
11:00 to 12:00	Andrea Sportiello Università degli Studi di Milano A Grassmann algebra related to spanning forests	Room 1

Thursday 1st May 2008
11:00 to 12:00	David Wagner University of Waterloo Algebraic numbers/chromatic roots working group	Discussion Room
14:00 to 15:00	Steven Noble Brunel University The clustering coefficient of a scale-free random graph	Room 1

Friday 2nd May 2008
11:00 to 12:00	Anthony Guttmann University of Melbourne Can we solve it? Some numerical tests revealing analytic structure.	Room 1
14:00 to 15:00	Bertrand Duplantier CEA/Saclay Large deviations and quantum gravity	Room 1

Thursday 8th May 2008
16:00 to 17:00	William Faris University of Arizona Trees versus connected graphs I	Room 1

Friday 9th May 2008
14:00 to 15:00	David Binnie Penman University of Essex Random randomly coloured graphs	Room 1

Thursday 15th May 2008
16:00 to 17:00	William Faris University of Arizona Trees versus connected graphs II	Room 1

Wednesday 21st May 2008
10:00 to 11:00	Fengming Dong Nanyang Technological University On the shameful conjecture	Room 2

Thursday 29th May 2008
11:00 to 12:00	Mihai Ciucu Indiana University On the interaction of defects in lattices	Room 1

Monday 2nd June 2008
17:00 to 18:00	Carsten Thomassen Technical University of Denmark Maps and graphs on surfaces	Room 1

Thursday 5th June 2008
16:00 to 17:00	David Jackson University of Waterloo Zero-free regions for multivariate Tutte polynomials	Room 1

Tuesday 10th June 2008
11:00 to 12:00	Julius Borcea Stockholm University Negative dependence and zeros of multivariate polynomials I	Room 2

Thursday 12th June 2008
11:00 to 12:00	Gordon Royle University of Western Australia Bounding chromatic roots of series parallel graphs in terms of maxmaxflow	Room 1

Tuesday 17th June 2008
11:00 to 12:00	Julius Borcea Stockholm University Negative dependence and zeros of multivariate polynomials II	Room 2

Wednesday 18th June 2008
10:00 to 11:00	The upper bound on number of graphs, with fixed number of vertices, that vertices can be coloured with n colours	Room 2
11:00 to 12:00	Julius Borcea Stockholm University Negative dependence and zeros of multivariate polynomials III	Room 2

Thursday 19th June 2008
11:00 to 12:00	Petter Branden KTH - Royal Institute of Technology Negative dependence and zeros of multivariate polynomials IV	Room 2

Friday 20th June 2008
11:00 to 12:00	A complexity dichtomy for partition functions with mixed signs	Room 2

Organisers

Peter Cameron Queen Mary University of London
Bill Jackson Queen Mary University of London
Alexander Scott University of Oxford
Alan Sokal New York University
David Wagner University of Waterloo

Speakers

Roger Emil Behrend Cardiff University
Julius Borcea Stockholm University
Petter Branden KTH - Royal Institute of Technology
Peter Cameron Queen Mary University of London
Mihai Ciucu Indiana University
Fengming Dong Nanyang Technological University
Bertrand Duplantier CEA/Saclay
William Faris University of Arizona
Graham Ernest Farr Monash University
Tatiana Gateva-Ivanova Bulgarian Academy of Sciences
Anthony Guttmann University of Melbourne
David Jackson University of Waterloo
Mark Jerrum Queen Mary University of London
Martin Loebl Charles University, Prague
Steven Noble Brunel University
David Binnie Penman University of Essex
Aldo Procacci Universidade Federal de Minas Gerais (UFMG)
Gordon Royle University of Western Australia
James Sellers Pennsylvania State University
Simone Severini University of Waterloo
Senya Shlosman Centre de Physique Théorique, Marseille
Alan Sokal
Andrea Sportiello Università degli Studi di Milano
Carsten Thomassen Technical University of Denmark
David Wagner University of Waterloo

Show All

Combinatorics and statistical mechanics

Programme theme

Support from the National Science Foundation

Preprints

Weighted enumeration of spanning subgraphs with degree constraints

A combinatorial proof of Rayleigh monotonicity for graphs

Zero-free regions for multivariate Tutte polynomials (alias Potts-model partition functions) of graphs and models

Enumeration of the degree sequences of non-separable graphs and connected graphs

Quantum spaces associated to multipermutation solutions of level 2

Counting 2-connected deletion-minors of binary matroids

Counting defective parking functions

Oligomorphic permutation groups

Sparse random graphs with clustering

The exact evaluation of the corner-to-corner resistance of an $M ×N$ resistor network: asymptotic expansion

Transforms and minors for binary functions

Computing Tutte polynomials

Workshops

Combinatorics and statistical mechanics - an introductory cross-disciplinary symposium

Zeros of chromatic, flow and other polynomials

Markov chain Monte Carlo methods

Combinatorial identities and their applications in statistical mechanics

Statistical-mechanics and quantum-field-theory methods in combinatorial enumeration

Combinatorial and probablistic inequalities

Seminars

Organisers

Speakers

Supported By

Combinatorics and statistical mechanics

Programme theme

Support from the National Science Foundation

Preprints

Weighted enumeration of spanning subgraphs with degree constraints

A combinatorial proof of Rayleigh monotonicity for graphs

Zero-free regions for multivariate Tutte polynomials (alias Potts-model partition functions) of graphs and models

Enumeration of the degree sequences of non-separable graphs and connected graphs

Quantum spaces associated to multipermutation solutions of level 2

Counting 2-connected deletion-minors of binary matroids

Counting defective parking functions

Oligomorphic permutation groups

Sparse random graphs with clustering

The exact evaluation of the corner-to-corner resistance of an $M ×N$ resistor network: asymptotic expansion

Transforms and minors for binary functions

Computing Tutte polynomials

Workshops

Combinatorics and statistical mechanics - an introductory cross-disciplinary symposium

Zeros of chromatic, flow and other polynomials

Markov chain Monte Carlo methods

Combinatorial identities and their applications in statistical mechanics

Statistical-mechanics and quantum-field-theory methods in combinatorial enumeration

Combinatorial and probablistic inequalities

Seminars

Organisers

Speakers

Supported By

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