Clay Mathematics Institute

Dedicated to increasing and disseminating mathematical knowledge

Probability and Statistical Physics in Two and More Dimensions

July 11 - August 7, 2010

Buzios, Brazil

Organizers: David Ellwood, Charles Newman, Vladas Sidoravicius, Wendelin Werner

In the past 10 to 15 years, various areas of probability theory related to rigorous statistical mechanics, disordered systems and combinatorics have enjoyed an intensive development.  A number of these developments deal with two-dimensional random structures.  The questions related to critical systems are two-fold: understanding large-scale properties of lattice-based models (on a periodic deterministic lattice or in the case where the lattice is itself random) and, on the other hand, being able to construct and manipulate a continuous object that describes direcly their scaling limits.

In the case of a fixed planar lattice, a number of conjectures originating in the physics literature have now been proved, but many questions remain open.  In the case of statistical physics on random planar graphs, sometimes referred to as quantum gravity, many results have been recently understood and a relation between discrete and continuous structures is now emerging.  The aim of this school is to provide a complete picture of the current state of the art in these and related topics.

Foundational Courses

Large Random Planar Maps and their Scaling Limits
Jean-Francois Le Gall (Paris-Sud) and Gregory Miermont (Paris-Sud)

SLE and Other Conformally Invariant Objects
Vincent Beffara (ENS Lyon)

Noise-sensitivity and Percolation
Jeffrey Steif (Chalmers) and Christophe Garban (ENS Lyon)


Random Geometry and Gaussian Free Field
Scott Sheffield (MIT)

Conformal Invariance of Lattice Models
Stanislav Smirnov (Geneve)

Integrable Combinatorics
Philippe Di Francisco (CEA Saclay)

Fractal and Multifractal Properties of SLE
Gregory Lawler (Chicago)

The Double Dimer Model
Rick Kenyon (Brown)

Random Polymers
Frank den Hollander (Leiden)

Self-avoiding Walks
Gordon Slade (British Columbia)