Dynamics, Probability, and Conformal Invariance

The study of dynamics in the plane has recently seen a surge in interest due to three recent breakthroughs: the Sullivan-McMullen-Lyubich proof of the Feigenbaum Universality, the introduction by O. Schramm of SLE processes, and the work of S. Smirnov on percolation. The fields of Holomorphic Dynamics, SLE, and Conformal Field Theory (CFT) are now seen to be closely linked, the glue being provided by renormalization arguments, conformal mappings, Brownian Motion, and other methods related to Conformal Invariance. Indeed, there is an emerging field where these different dynamical processes, as well as more classical areas in conformal mappings, are unified into a more general theory. Though it is still early in the game, much progress has been made. The workshop has brought together leading experts from the areas of SLE, Holomorphic Dynamics, Probability Theory, and Conformal Mappings to present the latest developments in these areas and search for further unification of the fields.