Schramm-Loewner Evolution (SLE) is the solution of the classical Loewner equation in complex analysis with a stochastic driving function defined in terms of a one-dimensional Brownian motion. Since it was introduced for the first time by Odded Schramm in 1999, SLE has been intensively studied by mathematicians and physicists. It has been proved or conjectured to be the scaling limits of various lattice models in statistical physics. In this talk, we will discuss the average generalized integral means spectrum of the whole-plane variant of SLE. This generalized spectrum has been introduced to give a unified framework to study the (expected) standard integral means spectrum of various functions in the SLE context. We will introduce the definition of the average generalized integral means spectrum of whole-plan SLE and a conjecture about the values of this spectrum. We then talk about the results so far obtained that confirm this conjecture and the Maximum principle method that were used to derive these results. This talk is based on joint works with Bertrand Duplantier, Thanh Binh Le and Michel Zinsmeister.

Meeting ID: 852 4277 3200 Passcode: 103121