An introduction to the CP-process for Furstenberg's intersection conjecture

This seminar is part of the weekly ergodic theory and dynamical systems seminar.

For two multiplicatively independent positive integers p and q, Furstenberg (2019) conjectured that the transformations px mod 1 and qx mod1 are transverse. This means that the Hausdorff dimension of the intersection of two closed invariant sets is bounded by the sum of their Hausdorff dimensions minus one. This conjecture has been independently proven by Meng Wu and Pablo Shmerkin using different methods. In this talk, I will present the Conditional Probability (CP) process introduced by Furstenberg, which plays a key role in Meng Wu's proof, and briefly outline the main ideas behind Wu's proof.