A survey on the Hausdorff dimension of intersections

Abstract

Let $A$ and $B$ be Borel subsets of the Euclidean $n$-space with $\dim A+\dim B>n$. This is a survey on the question: what can we say about the Hausdorff dimension of the intersections $A\cap (g(B)+z)$ for generic orthogonal transformations $g$ and translations by $z$.

This survey is based on the talk I gave in Karoly Simon's 60+1 birthday conference in Budapest in June 2022. Version 2 improves theorems of Section 6 by removing positive lower density assumtions