Suppose f is a function with Fourier transform supported on the unit sphere in Rd. Elias Stein conjectured in the 1960s that the Lp norm of f is bounded by the Lp norm of its Fourier transform, for any p>2d/(d−1).  We propose to study this conjecture using Bourgain-Demeter decoupling theorem and incidence estimates for tubes. In this talk, we will describe a geometric conjecture, the two-ends Furstenberg conjecture, that would imply Stein's restriction conjecture. We prove it in R2 and obtain a partial result in R3 that implies the restriction estimate in R3 for any p>3+1/7. This restriction estimate implies Wolff's hairbrush Kakeya bound: any Kakeya set in R3 has Hausdorff dimension at least 5/2.