Restriction Estimates Using Decoupling Theorem and Incidence Estimates for Tubes

Watch a 56-minute mathematical physics lecture from the Institute for Advanced Study where Hong Wang from New York University explores Stein's restriction conjecture through the lens of the Bourgain-Demeter decoupling theorem and tube incidence estimates. Delve into the geometric aspects of the two-ends Furstenberg conjecture and its implications for Stein's restriction conjecture, examining proven results in R2 and partial findings in R3 that lead to restriction estimates for p>3+1/7. Learn how these mathematical concepts connect to Wolff's hairbrush Kakeya bound, demonstrating that Kakeya sets in R3 have a Hausdorff dimension of at least 5/2. Explore the fundamental question posed by Stein in the 1960s regarding the relationship between a function's Lp norm and its Fourier transform when supported on a unit sphere in Rd.