讲座题目☂️🚰：Hoffman's limit theorem 主讲人🕵🏿：Akihiro Munemasa 教授 主持人：詹兴致 教授 开始时间🦡：2019-09-26 15:00:00 结束时间🙋🏿：2019-09-26 16:00:00 讲座地址：闵行数学楼401报告厅 主办单位：数学科学学院
报告人简介： Akihiro Munemasa（宗政昭弘）教授1961年出生于日本，1989年在美国Ohio州立大学获得博士学位，是1990年度Heizaemon Honda Fellow。他从2003年至今任日本东北大学教授。 Munemasa教授在组合设计👩🏻🦱、编码理论和代数图论等领域做出了重要贡献🏌️♀️。他已经发表学术论文100篇。他的成就获得了同行的赞赏，例如，他是著名专业杂志 Algebraic Combinatorics 的主编以及 Graphs and Combinatorics的编委👨🏽💼。他多次在国际会议上做邀请报告🍞。 报告内容： A.J. Hoffman first gave a brief description of a theorem about the behavior of the smallest eigenvalues of graphs when some of the vertices are replaced by cliques of increasing size. Hoffman claimed that this result would appear later in a joint paper with Ostrowski, but such a paper has never get published. Instead, Hoffman proved a slightly more general, signed graph version of the result, but the proof remained sketchy. In this talk, we formulate this result as a theorem for general Hermitian matrices purely in terms of matrices, so as to be applicable for Hermitian adjacency matrices of digraphs. As an application, we show a signed analogue of Hoffman's theorem which states that a signed graph with smallest eigenvalue greater than -2 and large enough minimum degree is necessarily switching equivalent to a complete graph.Our proof is shorter than Hoffman's original which only deals with unsigned graphs, because we make use of the classification of integrally represented signed graphs with smallest eigenvalue greater than -2 established GK.This is joint work with Alexander Gavrilyuk, Yoshio Sano and Tetsuji Taniguchi. |
