报告一：Discrete integrable system and its application in
computational mathematics
主讲人：冯宝峰 （教授）德克萨斯大学数学与统计学院
简 介：冯宝峰教授从事应用数学、非线性波数值计算方面的研究，在可积系统和孤立子理论方面提出了超快光脉冲传播的模型方程和可积格子自适应算法，在国际知名期刊上发表论文70余篇，被引用超千次，通过清华大学和上海交通大学获批国家自然科学基金海外及港澳学者基金。
报告二：On classification of tau-symmetric integrable
Hamiltonian evolutionary PDEs
主讲人：张友金 （教授、长江学者）清华大学数学科学系
简 介：张友金教授主要从事数学物理与可积系统理论方面的研究，涉及仿射Weyl群轨道空间的几何、可积系统与Frobenius流形之间的内在联系、量子上同调和Gromov-Witten不变量理论中的Virasoro猜想以及可积系统的分类理论等方面，在Inven. Math.、Adv. Math.、Commun. Pure and Appl. Math.等国际顶级期刊发表论文十余篇。2000年获批国家杰出青年基金，2008年入选教育部长江学者奖励计划。
报告三：Matrix Integral, Hodge Integral, and Integrable system
主讲人：刘思齐 （教授）清华大学数学科学系
简 介：刘思齐教授从事数学物理与可积系统理论方面的研究，在Inven. Math.、Adv. Math.、Commun. Pure and Appl. Math.等国际顶级期刊发表论文十余篇。2012年获批国家优秀青年科学基金，2017年获批国家杰出青年基金。
时 间：2018年6月21日（星期四） 下午14:30-17:30
地 点：数学科学学院424室
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数学科学学院
2018年6月19日
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Discrete integrable system and its application in computational mathematics
Abstract： In this talk, we will give a review on recent development of discrete integrable system. We will firstly show that Hirota-Miwa equation, or the discrete Kadomtsev–Petviashvili (KP) equation, discrete modified KP equation and the discrete KP-Toda lattice equation are equivalent and can generate KP, modified KP and KP-Toda hierarchies as well as their Backlund transformations, respectively, by introducing Schur polynomial and Miwa transformation.Based on above findings, integrable discretizations of the real (complex) short pulse equation can be constructed, which can be used as self-adaptive moving mesh methods in numerical simulations of these equations.
张友金教授报告摘要：
On classification of tau-symmetric integrable Hamiltonian evolutionary PDEs
Abstract:We consider the problem of classification of integrable Hamiltonian deformations of the dispersionless KdV equation (also called the Hopf equation). We conjecture that such deformations are parametrized by an infinite sequence of functions of one variable, and give evidences to support this conjecture. If we impose the additional condition that the associated deformed integrable hierarchy possesses a tau structure, then we conjecture that these deformed integrable hierarchies are parameterized by an infinite sequenceof constants. We also give application of these integrable hierarchies to the study of Hodge integrals.
刘思齐教授报告摘要：
Matrix Integral, Hodge Integral, and Integrable system
Abstract: Matrix integral is a classical topic in mathematics. It is introduced by physicist E. Wigner, and has many interesting applications in physics, probability theory, mathematical statistics, numerical analysis, and number theory. It is revealed by the celebrated Witten conjecture that matrix integral is also the bridge among two-dimensional quantum gravity, the moduli space of stable curves, and the Korteweg-de Vries (KdV) hierarchy. Hodge integrals are the integrals of certain natural cohomological classes on the moduli space of stable curves, which are very important in modern mathematical physics. In our previous work, we showed that the generating function of certain Hodge integrals is related to the GUE matrix model and the Volterra hierarchy. We also conjecture a generalization of this correspondence. Recently, we prove this generalization.
