Abstract: We consider generic translation flows corresponding to Abelian differentials on flat surfaces of genus $g\ge 2$. These flows are weakly mixing by the Avila-Forni theorem. Recently Forni obtained Hoelder estimates on spectral measures for almost all translation flows, following earlier work by Bufetov and myself in genus two. Combining Forni's idea with our methods, we extended our proof to the case of arbitrary genus $g\ge 2$. It is based on a vector form of the Erd\H{o}s-Kahane argument, which I will try to explain.
This is a joint work with A. Bufetov.