Combinatorics and Statistical Mechanics

by Cambridge University

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.Read more at: www.newton.ac.uk/programmes/CSM/

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Recent Episodes
  • A bijection between subgraphs and orientations based on the combinatorics of the Tutte polynomial
    Apr 21, 2008 – 53:15
  • A bijection for covered maps on orientable surfaces
    Apr 30, 2008 – 57:46
  • A birthday paradox for Markov chains, with an optimal bound for collision in the Pollard Rho algorithm for discrete logarithm
    Apr 1, 2008 – 24:33
  • A Grassmann algebra related to spanning forests
    May 12, 2008 – 01:28:02
  • A Markov chain for certain triple systems
    Mar 27, 2008 – 34:22
  • A new probability inequality and some optimal concentration results
    Mar 27, 2008 – 37:34
  • A rosetta stone: combinatorics, physics, probability
    Apr 28, 2008 – 47:55
  • A simple resummation method for cluster expansions
    Feb 7, 2008 – 32:37
  • Alexander-Conway polynomial, milnor numbers, and the Pfaffian matrix-tree theorem
    Apr 25, 2008 – 01:07:21
  • Algebraic structure of the q-Knizhnik-Zamolodchikov equation on a segment, partial sums and punctured plane partitions
    May 1, 2008 – 01:04:56
  • Algorithms and complexity I
    Jan 28, 2008 – 01:10:06
  • Algorithms and complexity II
    Jan 28, 2008 – 01:11:33
  • Alternating sign matrices from a physicist point of view
    May 2, 2008 – 01:06:23
  • Alternative tableaux, permutations and partially asymmetric exclusion process
    May 7, 2008 – 01:10:18
  • An extensor tree theorem and a Tutte identity for graphs with distinguished port edges
    Apr 22, 2008 – 51:24
  • An introduction to dynamic critical phenomena and cluster algorithms
    Apr 1, 2008 – 39:34
  • An introduction to the Mayer expansion
    Apr 21, 2008 – 01:07:45
  • Analyticity of the pressure of the hard-sphere gas
    Apr 22, 2008 – 45:40
  • Asymptotic enumeration of contingency tables
    Mar 27, 2008 – 30:15
  • Bank sampling: a practical proposal for sampling from isolated maxima with the Metropolis algorithm
    Apr 2, 2008 – 31:23
  • Boundary partitions in trees and dimers
    May 8, 2008 – 01:05:21
  • Bounding chromatic roots of series parallel graphs in terms of maxmaxflow
    Jul 1, 2008 – 01:04:36
  • Bounds for the numner of matchings in regular graphs
    Feb 1, 2008 – 27:49
  • Can extra updates delay mixing?
    Mar 27, 2008 – 46:38
  • Can we solve it? Some numerical tests revealing analytic structure.
    May 13, 2008 – 01:15:17
  • Card shuffling and Diophantine approximation
    Apr 2, 2008 – 29:57
  • Chromatic factorisation of graphs
    Jan 31, 2008 – 33:07
  • Chromatic polynomials and a second Hamiltonian cycle
    Jan 31, 2008 – 01:04:58
  • Chromatic roots and fibonacci numbers
    Jan 30, 2008 – 23:20
  • Chromatic zeros for some recursively defined families of graphs
    Feb 7, 2008 – 31:20
  • Cluster expansions (a historical overview)
    Apr 15, 2008 – 01:03:09
  • Cluster expansions for hard-core systems: I introduction
    Feb 6, 2008 – 58:49
  • Cluster expansions for hard-core systems: II convergence criteria
    Feb 6, 2008 – 01:05:16
  • Colouring random graphs randomly
    Mar 31, 2008 – 31:31
  • Combinatorial enumeration I
    Jan 24, 2008 – 59:09
  • Combinatorial enumeration II
    Jan 25, 2008 – 01:03:35
  • Combinatorial identities and the correlation function gaps in dimer packings
    Apr 24, 2008 – 47:47
  • Combinatorics and quantum information theory
    Mar 26, 2008 – 01:01:23
  • Complex roots of chromatic polynomials
    Feb 8, 2008 – 01:09:16
  • Complex zeros of the chromatic and Tutte polynomials
    Jan 31, 2008 – 01:08:56
  • Conformal field theory I
    Jan 28, 2008 – 01:08:36
  • Conformal field theory II
    Jan 29, 2008 – 01:09:19
  • Conformal field theory III
    Jan 30, 2008 – 01:07:05
  • Conformal invariance and universality in the 2D lsing model
    May 6, 2008 – 01:09:28
  • Connections between combinatorics and statistical mechanics
    Mar 18, 2008 – 49:12
  • Connes-Kreimer Hopf algabra for non-commutative field theory
    Apr 25, 2008 – 43:38
  • Constructive field theory without tears
    Apr 28, 2008 – 48:52
  • Constructive resolution of two conjectures on real chromatic roots
    Feb 1, 2008 – 58:27
  • Counting lattice paths with the kernel method
    May 9, 2008 – 01:09:00
  • Counting partially directed walks in a symmetric wedge
    Apr 29, 2008 – 51:17
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