On the exceptional set for absolute continuity of Bernoulli convolutions

The title of the talk is the title of a paper by Pablo Shmerkin, in which he significantly strengthens the famous result of Solomyak. He proves that the exceptional parameters for the Erdos problem (i.e. the parameters $\lambda$ for which the Bernoulli convolution $\sum \pm \lambda^n$ with signs chosen with probability (1/2,1/2), independently, is not absolutely continuous) have Hausdorff dimension 0. The paper refers to some recent results of Hochman and the author, so I probably won't be able to present the full picture, but I should be able to at least give an introduction to this theory.