### Theme of Workshop:

The workshop will be concerned broadly with combinatorial and probabilistic inequalities and their applications to problems arising in combinatorics, probability theory, and the analysis of statistical mechanics models. Examples of such inequalities include those of Fortuin-Kasteleyn-Ginibre, of Ahlswede-Daykin, of van den Berg-Kesten-Reimer, other inequalities expressing positive or negative correlations, inequalities on higher moments, isoperimetric inequalities, eigenvalue inequalities, upper or lower bounds on asymptotic growth rates, critical exponents, or critical probabilites, and so on. Such inequalities are applied to questions on the combinatorics of graphs, matroids, and partial orders, and to probabilistic and statistical mechanical models such as percolation, Potts models and random cluster models, lattice gases, exclusion processes, random matrix models, and so on.

The workshop will provide a venue for some of the leading researchers in these fields to share recent ideas and to collaborate on approaches to many of the unsolved problems in this area. It will also feature some survey lectures intended to provide a snapshot of the current state of the art for younger researchers interested in these subjects. The topics will be of interest to combinatorialists, probabilists, mathematical and theoretical physicists, and computer scientists.

### Keynote speakers will include:

Rob van den Berg (*CWI*), Béla Bollobás (*Cambridge, Memphis*), Jeff Kahn (*Rutgers*), Alan Sokal (*NYU, UCL*) and Dominic Welsh (*Oxford*).

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