Linear projections of the product of a ª2 and a ª3 invariant measure

Given a compact set X in the plane, the image of X under orthogonal projection to almost every line has the maximal possible Hausdorff dimension, i.e. min{1,dim(X)}. An old conjecture of Furstenberg’s predicts that when X=AxB, and A,B are x2 and x3 invariant sets, respectively, then this should hold for every line except the trivial exceptions (those parallel to the axes). I will describe a proof of this and its measure equivalent. This is joint work with Pablo Shmerkin.