Lukas Schoug: A multifractal SLE_\kappa(\rho) boundary spectrum

The Schramm-Loewner evolution (SLE) is a family of fractal curves, conjectured (and in many cases proven) to be the scaling limit of interfaces in models from statistical mechanics. In this talk, we consider a generalisation of SLE, and prove an almost sure multifractal boundary spectrum for this family, that is, find the dimension of the set of points where the curve intersects the boundary at a prescribed “angle”. This is done via a coupling with the Gaussian Free Field, in which the SLE curves arise as flow lines.