Conformal Invariance, Discrete Holomorphicity and Integrability

The general scope of the meeting is modern methods of random geometry, integrability and conformal invariance applied to statistical mechanics.

Many important lattice models of statistical mechanics are exactly solvable or integrable. At the critical point of a continuous phase transition these models are expected to have conformally invariant scaling limits. The physics research of these systems has been very active since 1980’s: conformal field theory is used to describe the scaling limit and exact solution of the lattice model is often based on the integrable structure in the form of commuting transfer matrices obtained from solutions to the Yang-Baxter equations.

Promising new mathematical ideas include conformally invariant random geometry, especially the random curves known as Schramm-Loewner Evolutions (SLE). A key advance is the use of discrete harmonic or discrete holomorphic observables of the lattice models for proving existence and conformal invariance of scaling limits. The purpose of this meeting is to bring together mathematical physicists with expertise in probability theory, analysis, integrable systems, combinatorics and representation theory, in order to advance further the discrete holomorphicity method, its relation to integrability and conformal field theory and related topics.