报告题目：On peakons, Toda lattices and related orthogonal polynomials, random matrix ensembles

报告人：常向科，中国科学院数学与系统科学研究院

报告时间：2021年7月6号（星期二）下午14:00-15:30

腾讯会议：572 283 2445

密码：123456

摘要：A class of nonlinear integrable PDEs admit some special weak solutions called ``peakons'', which are characterised by ODE systems, namely peakon lattices. The celebrated Toda lattice was originally obtained as a simple model for describing a chain of particles with nearest neighbor exponential interaction and  has been generalized in different directions. Both of the peakon and Toda lattices could be regarded as isospectral deformations related to certain orthogonal functions. In fact, for some initial value problems, these lattices can be explicitly solved by use of inverse spectral method involving certain ``orthogonality, approximation problems and continued fractions. In this talk, I will illustrate this picture with some typical examples and also show how they correspond to the partition functions of random matrix ensembles.