Avelio Sepulveda, University of Chile: An elementary approach to quantum length of SLE

Speaker

Avelio Sepulveda, University of Chile




Abstract

Joint work with Ellen Powell. In this talk, I will present an elementary proof establishing the equality of the right and left-sided √κ-quantum lengths for an SLE(κ) curve, where κ∈(0,4]. This is done by equating these measures to the (√ κ/2)-Gaussian multiplicative chaos with reference measure given by half the conformal Minkowski content of the curve times an explicit constant.  This proof relies on a novel “one-sided” approximation of the conformal Minkowski content, which is compatible with the conformal change of coordinates formula.