报告人：赖虹建教授、Ren-Cang Li（李仁仓）教授
报告时间：2019年1月4日上午9:30-11:30
报告地点：理学楼 344室
报告人及内容简介：
赖虹建教授、1983-1988在美国密执安韦恩州立大学获数学博士学位，导师为JCTB杂志的编辑凯特林（Catlin）教授。获得过1996年西弗吉尼亚大学文理学院最优科研奖和2006年西弗吉尼亚大学最优教师奖。是西弗吉尼亚大学第一个获得此项奖励的华人教授。曾任“离散数学”杂志客座编委，现任Journal of Discrete Mathematics以及Graph andCombinatorics等杂志的编委。 赖虹建教授已完成了两部专著，分别是由克鲁亚学术出版社出版的“图与组合学中的矩阵论” 和由高等教育出版社出版的“拟阵论”，并在各类数学杂志上发表学术论文200多篇，其中SCI检索的170多篇。
Title: Graph Eigenvalues and Graphical Properties
Abstract: We will present some of the recent progresses in using grapheigenvalues to predict graphical properties. Cioaba and Wong in [LAA, 437(2012) 630–647] posed a conjecture on using the secondlargest eigenvalue of a graph to describe the maximum number of edge-disjointspanning trees. In [Electronic Journal of Linear Algebra, 34 (2018) 428-443] A.Abiad et al proposed an open problem suggesting to use the second largesteigenvalue of a graph to predict the connectivity of the graph. In this talk,we will report the recent progresses towards the above-mentioned conjecture andopen problems, as well as other related studies on relating graph eigenvaluesto graph structural properties.
Ren-Cang Li（李仁仓）教授。1995年毕业于加州大学伯克利分校University of California atBerkeley，获应用数学博士学位。现为美国德州大学阿灵顿分校（University of Texas atArlington）教授，长期从事数值代数、科学计算、微分方程数值解法等领域的研究。在SIAM J SCICOMPUT, Numerische Mathematik, Math. Comp., SIAM J. Matrix Anal. Appl.,Numerical Linear Algebra with Applications, BIT Numerical Mathematics等国际著名期刊上发表学术论文一百多篇。）
Title：Eigenspace Perturbation, a Brief Survey
Abstract：Eigenspace perturbation is a well-studiedtopic. Well-known results include Davis-Kahan sin_heorems for the Hermitianeigenvalue problem and their extensions to the singular value problem, polardecomposition, the generalized eigenvalue problem, and the relativeperturbation theory that has been an active research in the last two decades. Recently,the eigenspace perturbation has found an important application in the study ofthe Nonlinear Eigenvalue Problem with eigenvector nonlinearity. In this talk,we will survey various fundamental results and the basic techniques in theirestablishments.
