Jerusalem Mathematics Colloquium

Thursday, 21st May 2009, 4:00 pm
Mathematics Building, Lecture Hall 2

Mike Hochman

"Local entropy and projections of Cantor sets"


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=A?B, and A,B are ?2 and ?3 invariant sets in [0,1], 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.

Light refreshments will be served in the faculty lounge at 3:30.

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