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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...

I will tell the story of a mathematical problem which can be understood and tested by a child, yet which has resisted solution for over a century, in spite of the efforts of many prominent mathematicians. I will describe in parallel the development...