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Abstract |
Two compact sets E,F of the real line are said to be strongly transverse if for each u and t, the Hausdorff dimension (dim) of the intersection of E and uF+t is bounded by dim(E)+dim(F)-1 or 0, whichever is larger. In the late 60’s, Furstenberg conjectured that two closed sets E,F of [0,1] are strongly transverse if E is invariant under multiplication by 2 (mod 1) and F is invariant under multiplication by 3 (mod 1). In this talk, we will recall some recent progress regarding this conjecture and present a solution. |
