王虹 - Restriction Estimates Using Decoupling Theorem and Incidence Estimates ...

作者: 筑桥者Hagi

作者简介: La découverte est le privilège de l’enfant.

描述: https://youtu.be/F4Xn9T5gGPI Analysis and Mathematical Physics 2:30pm|Simonyi Hall 101 and Remote Access Topic: Restriction Estimates Using Decoupling Theorem and Incidence Estimates For Tubes Speaker: Hong Wang Affiliation: New York University Date: January 28, 2025  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 greater than 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 greater than 3+1/7. This restriction estimate implies Wolff's hairbrush Kakeya bound: any Kakeya set in R3 has Hausdorff dimension at least 5/2.