Systems of equiangular lines, Seidel matrices and adjacency matrices
报告题目(Title)： Systems of equiangular lines, Seidel matrices and adjacency matrices
报告人(Speaker)：Jack Koolen 教授 (中国科学技术大学)
地点(Place)：腾讯会议：945 939 048
时间(Time)：2021-6-4, 下午 4:00-5:00.
邀请人(Inviter)：徐敏
报告摘要
It is known that large systems of equiangular lines with common angle $\arccos{1/\alpha}$ are closely related with Seidel matrices $S$ with smallest eigenvalue $-\alpha$ such that $S + \alpha I$ has low rank. In this talk I will introduce the notion of a switching root and show how we can use the switching root to relate adjacency matrices and Seidel matrices. If time permits I will also discuss some new maximal connected graphs with minimal eigenvalue -3, that is, any proper connected supergraph of such graph has smallest eigenvalue less than -3. This is based on joint work with Meng-Yue Cao (Beijing Normal University), Akihiro Munemasa (Tohoku University), Kiyoto Yoshino (Tohoku University) and Brhane Gebremichel (University of Science and Technology of China).
主讲人简介
Jack Koolen is currently a full professor at the University of Science and Technology of China. He received his Ph.D. from Eindhoven University of Technology in 1994 under supervision of Prof Andries Brouwer. After a few post doc positions in for example Oxford University and Kyushu University, he became an associate professor in POSTECH in Pohang Korea. Since 2013 he is a full professor at the University of Science and Technology of China. His main interest is in algebraic graph theory especially distance-regular graphs. Recently he also got interested in graphs with fixed smallest eigenvalues. He has co-authored a book on phylogenetic combinatorics. He serves as a managing editor of Graphs and Combinatorics also.
