会议时间：2022-10-27(周四) 13:30开始
会议地点：腾讯会议，会议号：517-614-507
报告题目1： Existence of Global Solutions to the Nonlocal NLS Equation with the Inverse Scattering Transform Method
报 告 人：范恩贵 （复旦大学 教授）
报告摘要：With inverse scattering and operator theory, we prove the existence of global solutions to the Cauchy problem for the integrable nonlocal nonlinear Schrodinger equation in the Sobolev space 
with -small norm assumption. Further we establish the bijectivity and Lipschitz continuity of the direct and inverse scattering map from the initial data to reflection coefficients
报告人简介：范恩贵，复旦大学教授、博士生导师,上海市曙光学者，主要研究方向：可积系统和反散射理论；主持国家自然科学基金、上海曙光计划等多项研究课题。 在 《Adv. Math. 》、《SIAM J. Math. Anal.》、 《J. Diff. Equ.》等国际重要期刊发表论文100余篇。应邀访问美国密苏里大学、日本京都大学等。曾获教育部自然科学二等奖、上海市自然科学二等奖、复旦大学谷超豪数学奖。
报告题目2： Higher Order Airy and Painlevé Asymptotics for the mKdV Hierarchy
报 告 人：张仑 （复旦大学 教授）
报告摘要: In this talk, we consider Cauchy problem for the modified Korteweg-de Vries hierarchy on the real line with decaying initial data. Using the Riemann--Hilbert formulation and nonlinear steepest descent method, we derive a uniform asymptotic expansion to all orders in powers of $t^{-1/(2n+1)}$ with smooth coefficients of the variable $(-1)^{n+1}x((2n+1) t)^{-1/(2n+1)}$ in the self-similarity region for the solution of $n$-th member of the hierarchy. It turns out that the leading asymptotics is described by a family of special solutions of the Painlevé II hierarchy, which generalize the classical Ablowitz-Segur solution for the Painelvé II equation and appear in a variety of random matrix and statistical physics models. We establish the connection formulas for this family of solutions. In the special case that the reflection coefficient vanishes at the origin, the solutions of Painlevé II hierarchy in the leading coefficient vanishes as well, the leading and subleading terms in the asymptotic expansion are instead given explicitly in terms of derivatives of the generalized Airy function. This talk is based on a joint work with Lin Huang.
报告人简介：张仑，复旦大学数学科学学院教授；加入复旦大学之前，在香港城市大学获得博士学位，之后前往比利时鲁汶大学从事博士后研究工作。主持包括“优青”在内的多项国家自然科学基金，上海市东方学者、东方学者跟踪计划获得者。在CPAM，CMP等高水平杂志上发表论文多篇。研究方向Riemann-Hilbert问题，随机矩阵，渐进分析，逼近论等
