Furstenberg sets estimate in the plane

Abstract

We fully resolve the Furstenberg set conjecture in ${\mathbb{R}}^2$, that a $(s,t)$-Furstenberg set has Hausdorff dimension $\ge \min (s+t,\frac{3s+t}{2},s+1)$. As a result, we obtain an analogue of Elekes' bound for the discretized sum-product problem and resolve an orthogonal projection question of Oberlin.

23 pages. v2: fixed small typo in abstract and added more details to arguments, main results unchanged