报告一：Frank W. Nijhoff

报告题目：Direct linearization and KP type integrable systems
报告人：    Frank W. Nijhoff    英国利兹大学
主持人：    陈勇
报告时间：2019年4月4日  周四13:00-14:00
报告地点：中北校区数学馆201

报告摘要：
Probably the most popular derivation of the KP hierarchy is the one formulated by M. Sato using pseudo-differential operators. However, an alternative formulation exists on the basis of the direct linearization (DL) approach pioneered by researchers in the 1980s. The latter has some distinct advantages over the Sato approach, e.g. that it doesn't need to refer to a specific singled-out variable in terms of which the hierarchy is defined, and that it makes the multidimensional consistency more manifest. The talk provides a short review of the DL formulation of both continuous and discrete KP hierarchies, in particular the presentation of a 'universal' integrable system.

报告人简介：
Frank W. Nijhoff，荷兰莱顿大学博士，现为利兹大学数学学院教授、博士生导师、英国物理学会会士（Fellow of the Institute of Physics），长期从事离散可积系统、椭圆函数、差分方程等领域的相关研究，是可积系统领域国际权威。Nijhoff教授在《Communications in Mathematical Physics》、《International Mathematics Research Notices》、《Proceedings of the Royal Society》、《Nonlinearity》等国际一流数学物理期刊上累积发表论文100余篇，主持英国EPSRC基金多项。2012年当选为英国皇家学会Leverhulme Trust Senior Research Fellow。曾担任著名期刊《Journal of Physics A》数学物理板块主编，现为可积系统权威期刊《Journal of Integrable Systems》主编。

报告二：Allan P. Fordy

报告题目：Super integrability: an overview
报告人：    Allan P. Fordy  英国利兹大学
主持人：    唐晓艳
报告时间:   2019年4月4日  周四14:00-15:00
报告地点：中北校区数学馆201

报告摘要：
This talk starts with an expository description of what superintegrability is and how it differs from complete integrability. Using the system of two harmonic oscillators we see that in the non-resonant case we have only 2 first integrals, with quasi-periodic motion. The resonant case is superintegrable and the additional integrals give us periodic motion, with Lissajous figures being described by algebraic curves, being the level sets of the first integrals. In the quantum case this leads to degeneracy of the eigenvalues, with commuting operators laddering us between the eigenfunctions. The main part of the talk will be about the classical case and concentrate on how to build superintegrable systems with kinetic energies defined on various geometric spaces. 

报告人简介：
Allan P. Fordy，伦敦国王学院博士，现为利兹大学数学学院教授、博士生导师。Fordy教授在非线性数学物理多个领域作出过开拓性贡献，例如非线性薛定谔方程与二维Toda方程的代数分类、孤立子方程的Lax表示，以及可积系统中的Cluster代数等。在《Communications in Mathematical Physics》、《Physica D》、《Nonlinearity》等数学权威期刊上发表80余篇学术论文。曾担任数学物理著名期刊《Physics Letters A》主编长达30余年，现为知名期刊《SIGMA》编委。

报告三：Oleg Chalykh

报告题目：KP hierarchy and bispectral problem
报告人：    Oleg Chalykh  英国利兹大学
主持人：    傅蔚
报告时间：2019年4月4日  周四15:00-16:00
报告地点：中北校区数学馆201

报告摘要：
An ordinary differential operator is called bispectral if it admits a family of eigenfunctions which at the same time are eigenfunctions of some differential operator in the spectral variable. The bispectral problem posed by Duistermaat and Grunbaum asks for a classification of bispectral operators. It has beautiful connections with several areas of mathematics, in particular with nonlinear evolutionary equations. I will survey the link between the rational solutions to the KP hierarchy and bispectral operators. I will then discuss how this link can be generalised.
报告人简介：
Oleg Chalykh，博士毕业于莫斯科州立大学Novikov学派，康奈尔大学博士后，现为利兹大学讲师、博士生导师。Chalykh博士在可积系统、特殊函数、代数表示论等领域中作出过诸多开拓性贡献，在《Communications in Mathematical Physics》、《Advances in Mathematics》等顶级数学期刊上发表过多篇重要论文。