报告题目一：The Cauchy two-matrix model, C-Toda lattice and CKP hierarchy
报告时间：2019年11月23日09:05--09：50
报告地点：理学院一楼报告厅
报告人：李春霞
报告人简介: 李春霞，中科院计算数学所博士，首都师范大学数学科学学院教授，主要从事数学物理等方面的研究。先后主持多项国家自然科学基金项目，北京市自然科学基金项目等。
报告摘要：In my talk, I will first give a brief review on some known results of the Cauchy bi-orthogonal polynomials. Starting from the symmetric reduction of Cauchy biorthogonal polynomials, we derive the Toda equation of CKP type (or the C-Toda lattice) as well as its Lax pair by introducing time flows. Then, matrix integral solutions to the C-Toda lattice are extended to give solutions to the CKP hierarchy which reveals the time-dependent partition function of the Cauchy two-matrix model is nothing but the Tau-function of the CKP hiearchy. At last, the connection between the Cauchy two-matrix model and Bures ensemble is established from the point of view of integrable systems.
报告题目二：离散可积系统的有理解
报告时间：2019年11月23日09:50—10：35
报告地点：理学院一楼报告厅
报告人：张大军
报告人简介: 张大军，上海大学数学系教授，博士生导师。目前主要研究离散可积系统。SIDE (Symmetries and Integrability of Difference Equations) 会议指导委员会委员。2004年起先后作为国家公派留学生和访问学者访问芬兰Turku大学物理系、英国Leeds大学非线性科学中心、York大学、Loughborough大学、Glasgow大学、剑桥牛顿数学研究所、美国Texas大学(Pan-American)等，并先后主持多项国家自然科学基金面上项目。
报告摘要：Hirota-Miwa equation (also known as Hirota’s equation/discrete AKP equation) is one of general 3D discrete integrable equations. Tau function of this equation admits an algebraic form, composed of polynomials of discrete independent coordinates. In this talk I will discuss properties of such a tau function and its applications in constructing rational solutions of integrable quadrilateral equations (such as the Nijhoff-Quispel-Capel equation, equations in the Adler-Bobenko-Suris (ABS) list and some multi-quadratic ABS equations). The tau function obeys a bilinear superposition formula, which provides generalized Burchnall-Chaundy polynomials.
报告题目三：On integrable and nonintegrable spatial discrete NLS-type equations
报告时间：2019年11月23日10:50—11：35
报告地点：理学院一楼报告厅
报告人：朱佐农
报告人简介: 朱佐农，上海交通大学数学科学学院教授，博士生导师。学术研究领域是数学物理，研究方向是孤立子和可积系统理论，在连续和离散的可积系统的研究上取得若干重要进展。先后主持国家自然科学基金项目、上海市浦江人才计划项目和教育部留学回国人员基金项目。
报告摘要：In this talk, we will focus on the topic on integrable and nonintegrable spatial discrete nonlinear Schrodinger-type equations, including integrable and nonintegrable spatial discrete NLS equations, integrable and nonintegrable spatial discrete Hirota equations, and integrable and nonintegrable spatial discrete nonlocal NLS equations. This talk is based on the joint works with L.Y. Ma, C.Q. Song, J.L. Ji and Z.W. Xu.
报告题目四：Dbar method with applications to 1+1-dimensional integrable systems
报告时间：2019年11月23日14:30—15：15
报告地点：理学院一楼报告厅
报告人：范恩贵
报告人简介: 范恩贵，复旦大学教授、博士生导师，曾获教育部自然科学二等奖、上海市自然科学二等奖、国际“汤姆森路透卓越研究奖”、复旦大学谷超豪数学奖；主要研究方向是孤立子理论、可积系统、Riemann-Hilbert问题、正交多项式和随机矩阵理论；近年来，连续两届为国家“973”课题成员，并主持国家自然科学基金、上海曙光计划、上海曙光计划跟踪课题等多项研究课题。
报告摘要：In this talk, we first introduce short history of inverse scattering theory, then compare difference and connections among inverse scattering transformation, Riemann-Hilbert approach and dbar method. At last, we provide some applications in 1+1-dimensional integrable systems.
报告题目五：Binary Darboux transform method to the coupled Sasa-Satsuma equation
报告时间：2019年11月23日15:15—16：00
报告地点：理学院一楼报告厅
报告人：张海强
报告人简介: 张海强，上海理工大学理学院沪江学者教授。
报告摘要：The binary Darboux transformation method is applied to the coupled Sasa-Satsuma equations, which can be used to describe the propagation dynamics of femtosecond vector solitons in the birefringent fibers with third-order dispersion, self-steepening, and stimulated Raman scattering higher-order effects. An N-fold iterative formula of the resulting binary Darboux transformation is presented in terms of the quasideterminants. Via the simplest case of this formula, a few of illustrative explicit solutions to the coupled Sasa-Satsuma equations are generated from vanishing and non-vanishing backgrounds, which include the breathers, single- and double-hump bright vector solitons, and anti-dark vector solitons.