abstract: This seminar presents a recent work by Cheritat and Cheraghi. They prove that for quadratic Siegel disks, the difference between the Brjuno function and the logarithm of the conformal radius of the Siegel disk is a 12 Holder function when restricted to rotation numbers of high type (i.e., whose expansion in continued fractions only contains entries bigger that $N$ for some sufficiently large $N$).