报告题目：随机矩阵，正交多项式和潘勒韦方程

报告人：李传忠，山东科技大学数学与系统科学学院教授，博士生导师，山东省泰山学者。 2011年博士毕业于中国科学技术大学数学学院，美国俄亥俄州立大学联合培养博士。美国数学评论（Mathematical Reviews）特邀评论员、德国数学文摘（Zentralblatt Math）特邀评论员。曾任宁波大学数学与统计学院副院长，纪委书记。主要从事数学物理方向的研究工作。2015年入选宁波市领军和拔尖人才培养工程。2017年入选浙东青年学者计划。2021年入选山东省泰山学者青年专家。 主持国家自然科学基金面上项目2项和国家青年基金项目1项，主持浙江省自然科学基金面上项目2项。在国际数学物理类学术期刊( 如PLB,NPB,JNS,SAM,LMP,JGP,JMP,JPA,PRE等)上以第一作者或唯一通讯作者身份发表SCI论文100篇。多次应邀在美国等国家的国际会议上做报告，部分研究被科技金融时报头版头条报导。

摘要：Random matrix theory is important in statistics, wireless communication, finance and so on. Painlev´e transcendents are nowadays widely recognized as important special functions with a broad range of applications including integrable models, combinatorics and random matrix theory.  The study of random matrix theory (RMT) and orthogonal polynomials (OPs) for varying weights is often related to Painlev´e equations. For example, the properties of Hankel determinants which are always playing the most fundamental role in RMT, as well as the asymptotic behavior of the recurrence coefficients with respect to OPs, can be found by the analysis of the associated particular Painlev´e equations. The analysis of Hankel matrices occurs naturally in moment problems, which plays an important role in random matrix theory. The smallest eigenvalue is important since it gives great useful information on the nature of Hankel matrices with respect to given weights. Painlev´e equations possess many  similar interesting properties as integrable systems such as Lax pairs for which they act as compatibility conditions. The solutions of Painlev´e equations have special transformations (called Backlund transformations) which form interesting affine weyl groups.