Pablo Shmerkin: Intersections of self-similar sets

Abstract: Furstenberg conjectured in the 1960s that the intersections of $\times p$ and $\times q$ invariant sets are never "unexpectedly large" from the point of view of Hausdorff dimension. The conjecture was resolved affirmatively in 2019 by the speaker and independently by Meng Wu. While both proofs extend to intersections of a larger class of "homgeneous" self-similar sets, the non-homogeneous case had remained open. I will present joint work with Shunsuke Usuki in which we extend Furstenberg's intersection bound to a much broader class of pairs of self-similar sets.