Coefficient problem for whole-plane SLE

We revisit Loewner's method to prove the n=3 case of the Bieberbach conjecture in the case of whole-plane SLE. We show in particular that we can explicitly compute expectation and variance of the coefficients in infinitely many cases. We also investigate multifractal spectrum of whole plane SLE. This is a joint work with B.Duplantier, Nguyen Thi Phuong Chi and Nguyen Thi Thuy Nga.