讲座题目：8188www威尼斯学术报告

讲座人: Peter Clarkson 教授，Elizabeth Mansfield 教授，Stephen Anco 教授

讲座时间：08:30

讲座日期：2015-8-18

地点：雁塔校区 教学一楼303室

主办单位：8188www威尼斯 计算智能团队

讲座内容：

讲座题目1：Semi-classical orthogonal polynomials and the Painlevé equations

讲座时间：8：30-9：30

讲座人：Peter Clarkson 教授

讲座内容简介：

In this talk I shall discuss the relationship between the Painlevé equations and orthogonal polynomials with respect to semi-classical weights. It is well-known that orthogonal polynomials satisfy a three-term recurrence relation. I will show that for some semi-classical weights, the coefficients in the recurrence relation can be expressed in terms of Wronskians that arise in the description of special function solutions of a Painlevé equation. The orthogonal polynomials discussed will include semi-classical Laguerre and Hermite weights, a generalization of the Freud weight and an Airy weight.

讲座人简介：

Professor Peter Clarkson is currently the professor of Mathematics at University of Kent, UK . His research interests include Soliton theory, in particular the Painlevé equations and Painlevé analysis. Asymptotics, B?cklund transformations, connection formulae and exact solutions for nonlinear ordinary differential and difference equations, in particular the Painlevé equations. Orthogonal polynomials and special functions, in particular nonlinear special functions such as the Painlevé equations. Symmetry reductions and exact solutions of nonlinear partial differential equations.

Professor Clarkson is a participant in the NIST Digital Library of Mathematical Functions project, companion to the NIST Handbook of Mathematical Functions. He chairs the School’s Athena SWAN Committee and is a member of the University’s Athena SWAN working group. He also is a member of the London Mathematical Society’s Women in Mathematics Committee and chair of the steering committee for the LMS Good Practice Scheme. He was published more than 50 technical papers in refereed journals and conference proceedings.

讲座题目2：Discrete moving frames and multispace

讲座时间：9：30-10：30

讲座人：Elizabeth Mansfield 教授

讲座内容简介：

In this talk, I discribe the called discrete moving frames and multispace, which is essentially a sequence of moving frames with overlapping domains. I demonstrate a small set of generators of the algebra of invariants, which I call the discrete Maurer–Cartan invariants, for which there are recursion formulas. I show that this offers significant computational advantages over a single moving frame for our study of discrete integrable systems. I demonstrate that the discrete analogues of some curvature flows lead naturally to Hamiltonian pairs, which generate integrable differential-difference systems. In particular, I show that in the centro-affine plane and the projective space, the Hamiltonian pairs obtained can be transformed into the known Hamiltonian pairs for the Toda and modified Volterra lattices, respectively, under Miura transformations. I also show that a specified invariant map of polygons in the centro-affine plane can be transformed to the integrable discretization of the Toda Lattice. Moreover, I describe in detail the case of discrete flows in the homogeneous 2-sphere and I obtain realizations of equations of Volterra type as evolutions of polygons on the sphere.

讲座人简介：

Professor Elizabeth Mansfield is the professor of Mathematics at University of Kent, UK . Her research interests include Discrete Variational methods, with applications to geometric integration and musical composition and analysis. Moving frames. Symbolic analysis for nonlinear differential and difference equations.

Professor Mansfield is a member of the School’s Promotions Committee, vice-president of the Institute of Mathematics and its Applications (IMA), and chair of the IMA Research Committee. She has been on the Council of the London Mathematical Society (LMS), and is an editor of the LMS Journal of Computation and Mathematics. She served as a board member for the Journal of Foundations of Computational Mathematics. Some of her most important work has been published in international journals and conferences.

讲座题目3：New 2-component peakon equation arising from Hirota and Sasa-Satsuma hierarchies

讲座时间：10：30-11：30

讲座人：Stephen Anco 教授

讲座人简介：

Professor Stephen Anco is a full professor of Mathematics at University of Brock, Canada. Professor Anco received his B. S.

degree from Caltech, obtained his M. S. and Ph. D. degrees from Chicago. His research interests aremainly in Differential 

equations.Symmetries and conservation laws. Soliton theory. Mathematical physics.Symbolic computation. He has published more than 50 journal articlesand refereed conference proceedings.