（一）报告题目：调和分析在图像压缩中的作用

报告人：李文娟

报告时间：2024年5月11日 上午 09：00 - 10：00

报告地点：数理楼235教室 （Room 235）

报告摘要: 主要讲解调和分析中傅里叶变换、窗口傅里叶变换以及小波变换的发展以及基本性质，并且讲解这些变换在图像压缩中的作用。

（二）报告题目：Boundedness for maximal operators over hypersurfaces in $\mathbb{R}^3$

报告人：  王会菊 报告时间：2024年5月11日 上午 10：00-11:00

报告地点：数理楼235教室 （Room 235）

报告摘要:In this talk, we will discuss some recent progress in the study of maximal functions related to hypersurfaces with vanishing Gaussian curvature in $\mathbb{R}^3$. Firstly, we characterize the $L^p\rightarrow L^q$ boundedness of local maximal operators along homogeneous hypersurfaces. Moreover, weighted $L^p$-estimates are obtained for the corresponding global operators. Secondly, for a class of hypersurfaces that lack a homogeneous structure and pass through the origin, we attempt to look for other geometric properties instead of height of hypersurfaces to characterize the optimal $L^p$-boundedness of the corresponding global maximal operators.

（三）报告题目：Curved commutators in the plane

报告人:李康伟 报告时间：2024年5月11日 上午 11:00- 12:00

报告地点：数理楼235教室 （Room 235）

报告摘要:In this talk, I will talk about how we complete the $L^p$ boundedness theory of commutators of Hilbert transforms along monomial curves by providing the previously missing lower bounds. This optimal result now covers all monomial curves while previous results had significant geometric restrictions. We also, for the first time, develop the corresponding necessity theory for curves with non-vanishing torsion.