Boris Solomyak: Absolute continuity of non-homogeneous self-similar measures

In a joint work with P. Shmerkin and S. Saglietti, we prove that self-similar measures on the real line are absolutely continuous for almost all parameters in the super-critical region, in particular confirming a conjecture of S.-M. Ngai and Y. Wang. While recently there has been much progress in understanding absolute continuity for homogeneous self-similar measures, this is the first improvement over the classical transversality method in the general (non-homogeneous) case.