报告题目（一）：Uniform L^p bounds for Hilbert transforms and maximal operators along certain variable curves

报告人：万仁辉（南京师范大学）

报告时间：2023年5月6日14:00-15:00

报告地点：20-306

报告摘要：We will investigate the Hilbert transforms and the maximal operators along a class of variable non-flat polynomial curves (P(t), u(x)t) with measurable u(x), and then prove uniform L^p estimates for 1 < p < ∞. The proof is based on the time-frequency analysis techniques, the stationary and non-stationary phase methods in the theory of oscillatory integral; a new crucial estimate of some separate sets, which is motivated by a work of Victor Lie, will be mentioned.

报告题目（二）：Sharp maximal function estimates for Hilbert transforms along monomial curves in higher dimensions

报告人：万仁辉（南京师范大学）

报告时间：2023年5月6日15:00-16:00

报告地点：20-306

报告摘要：We will consider the maximal function for Hilbert transforms along monomial curves in higher dimensions and establish its sharp L^p estimates. Apart from the classical Chang-Wilson-Wolff inequality and some important point-wise estimates for the dyadic martingale difference operator,  the proof depends on recent progresses on the local smoothing estimate for averaging operator  by Ko-Lee-Oh and Beltran-Guo- Hickman-Seeger and a new maximal estimate for the  Mihlin-H\{o}rmander-type multiplier.

报告题目（三）：Stability and Inverse-closedness for Some Singular Integral Operators on Simple Graphs and Spaces of Homogeneous Type3.

报告人：陶祥兴（浙江科技学院）

报告时间：2023年5月6日16:00-17:00

报告地点：20-306

报告摘要：We will discuss the polynomial control on weighted stability bounds and inversion norms of localized matrices on simple graphs, and consider a family of singular integral operators in the Beurling algebra with kernels having mild singularity near the diagonal and certain Holder continuity property, and consider the inverse-closed Banach subalgebras of integral operators with kernels having certain off-diagonal decay can be informally interpreted as localization preservation under inversion, which is of great importance in applied harmonic analysis and engineering fields. This is a joint work with Qiquan Fang and Chang Eon Shin.

报告题目（四）：Asymptotic stability and large time behavior of some three dimension magnetohydrodynamic equations 

报告人：陈冬香（江西师范大学）

报告时间：2023年5月6日17:00-18:00

报告地点：20-306

报告摘要：In this paper, we investigate the stability issue and large time behavior of three dimensional magnetohydrodynamic equations with velocity damping and magnetic diffusion only in the $x_1$-direction near a background magnetic field. Due to the lack of the magnetic diffusion in two direction, this problem becomes more challenging. The classical anisotropic Sobolev techniques to deal with MHD equations with mixed dissipation fail here. Fortunately, combining anisotropic Sobolev techniques and some interpolation methods, we can establish  the asymptotic stability and explicit decay rates of the solutions to the three dimensional MHD equations mentioned above. The most difficult is to obtain the $L^1$-norm of $\|\nabla_h u\|_{L^\infty}$ in time. This work is joint with Jian Fangfang and Chen Xiaoli.

报告题目（五）：若干非线性系统的群分析和求解

报告人：沈守枫（浙江工业大学）

报告时间：2023年5月7日14:00-15:00

报告地点：20-306

报告摘要：介绍非线性系统的对称群分析理论。对于具体的例子介绍约化求解的方法。

报告题目（六）：The Rate of Convergence on Schr\odinger Operator

报告人：王梦（浙江大学）

报告时间：2023年5月7日15:00-16:00

报告地点：20-306

报告摘要：We will introduce   our works on the Rate Of Convergence On Schr\odinger Operator and Lp-estimate of Schrödinger maximal function.

报告题目（七）：Multipolar Hardy-Rellich inequality

报告人：金永阳（浙江工业大学）

报告时间：2023年5月7日16:00-17:00

报告地点：20-306

报告摘要：In this talk, we will firstly introduce the classical Hardy inequality, and then focus on some recent results on the multipolar Hardy-Rellich inequality.