中科院数学与系统科学研究院

数学研究所

调和分析及其应用研究中心

学术报告

调和分析和偏微分方程研讨班

报告人：Shukun Wu （Caltech）

题  目：A brief survey for Stein's restriction conjecture and the Kakeya conjecture（I）

时  间：2023.06.13（星期二）16:00-17:00

地  点：数学院南楼 N913

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题  目：A brief survey for Stein's restriction conjecture and the Kakeya conjecture（II）

时  间：2023.06.15（星期四）10:00-11:00

地  点：思源楼 S813

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题  目：A brief survey for Stein's restriction conjecture and the Kakeya conjecture（III）

时  间：2023.06.16（星期五）09:00-10:00

地  点：思源楼 S713

摘  要：Stein's Fourier restriction conjecture concerns the $L^p$ behavior of the Fourier transform of a given function. It is a central problem in Fourier analysis, and is connected to other branches of math ilke PDEs and number theory. In this talk, I will survey the restriction problem, as well as the ideas and techniques developed to attack this problem, including Kakyea type estimates, induction on scales, polynomial partitioning, and decoupling. In the follow-up lectures, l will survey some results, possibly in details, of the Kakeya conjecture.