报告题目：Local Smoothing: Methods and Recent Progress系列讲座

报告人：贺丹青副教授，复旦大学

报告时间：2026年9月19、20、21日（周六、周日、周一）8:30-10:30

报告地点：20-200

报告摘要：The local smoothing conjecture for wave equations is a central problem in modern harmonic analysis, closely connected with Fourier restriction theory and the Bochner–Riesz conjecture. In this mini-course, we will introduce the background of local smoothing and its relation to the Bochner–Riesz conjecture. We will then discuss several main tools in the subject, including wave packet decomposition, decoupling, and the broad–narrow argument. Finally, we will present recent approaches using incidence geometry, which lead to improved local smoothing estimates, including sharp results on Riemannian manifolds of odd dimensions. The course is intended to give both an introduction to local smoothing and an overview of the modern methods used to study it.

报告人简介：贺丹青，复旦大学副教授，国家级青年人才。主要从事调和分析中算子有界性的研究，研究成果包括多线性奇异积分算子的有界性、多线性乘子的有界性、锥乘子的点态收敛性。相关成果发表于Advances in Mathematics、Mathematische Annalen、Transactions of the American Mathematical Society等期刊，并获得重点研发计划青年科学家项目、上海市启明星项目等的资助。

邀请人：现代分析及其应用研究所