UBC Ergodic Theory Seminar: Boris Solomyak

From the work on Bernoulli convolutions by P. Erd\H{o}s in 1939 and up to the recent advances on self-similar measures by M. Hochman, P. Shmerkin, P. Varj\'u, and others, questions on absolute continuity and singularity remain to be a challenge. They are at the intersection of several fields, including fractal geometry, ergodic theory, and harmonic analysis. After a general introduction, I will discuss recent work with Adam \'Spiewak, where we obtain results on absolute continuity for ``typical'' self-similar measures in the plane.