Kakeya sets from lines in $S{L}_2$

Nets Hawk Katz, Shukun Wu, Joshua Zahl

We prove that every Kakeya set in ${\mathbb{R}}^3$ formed from lines of the form $(a,b,0)+\mathrm{span}(c,d,1)$ with $ad-bc=1$ must have Hausdorff dimension $3$; Kakeya sets…