时间：2025年5月27日14：00-16：45
地点：光华东主楼2201室
主持人：沈维孝教授
报告一：
报告人：张仑教授
题目：Transient asymptotics of the modified Camassa-Holm equation
时间：14：00-14：50
摘要: In this talk, we are concerned with long time asymptotics of the modified Camassa-Holm equation in three transition zones under a nonzero background. The first transition zone lies between the soliton region and the first oscillatory region, the second one lies between the second oscillatory region and the fast decay region, and possibly, the third one, namely, the collisionless shock region, that bridges the first transition region and the first oscillatory region. Under a low regularity condition on the initial data, we obtain Painlevé-type asymptotic formulas in the first two transition regions, while the transient asymptotics in the third region involves the Jacobi theta function. We establish our results by performing a nonlinear steepest descent analysis to the associated Riemann-Hilbert problem. Joint work with Taiyang Xu and Yiling Yang.
茶歇时间：14：50-15：05
报告二：
报告人：章嘉雯副教授
题目：Quasi-local algebras and measured asymptotic expanders
时间：15：05-15：55
摘要：Roe algebras are C*-algebras associated to metric spaces, which encode their large scale structures. These algebras play a key role in higher index theory, providing a bridge between geometry, topology and analysis. We study a quasi-local perspective on Roe algebras, which leads to a larger index algebra called the quasi-local algebra.
Based on the idea of quasi-locality, we introduce a graphic notion called measured asymptotic expanders which generalise the classic one of expanders. Using a structure theorem, we show that measured asymptotic expanders cannot be coarsely embedded into any Hilbert space and hence construct new counterexamples to the coarse Baum-Connes conjecture.
This is a joint project with Ana Khukhro, Kang Li, Piotr Nowak, Jan Spakula and Federico Vigolo..
报告三：
报告人：蔡圆副研究员
题目：Global current-vortex sheets in the two-dimensional ideal incompressible MHD
时间：15：55-16：45
摘要：The magnetohydrodynamic current-vortex sheet is a free boundary problem involving a moving free surface separating two plasma regions. We prove the global nonlinear stability of current-vortex sheet in the two dimensional ideal incompressible magnetohydrodynamics under the strong horizontal background magnetic field. This appears to be the first result on the global solutions of the free boundary problems for the ideal (inviscid and non-resistive) incompressible rotational fluids. The strong magnetic field plays a crucial role in the global in time stabilization effect. The proof relies on the understanding of the interplay between the dynamics of the fluids inside the domain and on the free interface, a design of multiple-level energy estimates with different weights, and the inherent structures of the problem. This is based on the joint work with Professor Zhen Lei.
复旦大学数学科学学院
非线性数学模型与方法教育部重点实验室
